Doctor of Philosophy (Ph.D.), Bowling Green State University, 2019, Statistics

In the case of analyzing multilevel, correlated, or longitudinal data, linear mixed models are often incorporated. Such models can be thought of an extension of linear models in the sense that the additional random components are introduced to capture the dependency in observations. In practice, missing data occur in many disciplines, especially in the area of longitudinal studies where observations are taken repeatedly over time on samples in an experiment. Our primary goal in the dissertation is to propose an approach to estimation and model selection in linear mixed models when missing data present. The dissertation pays particular attention to the multivariate normal models. With such models, we propose an approach that incorporates the missingness in an indicator matrix and develop likelihood-based estimators under two specific covariance structures: compound symmetric and first-order autoregressive (AR(1)). Distinguishing from the existing maximum likelihood estimation (MLE) that relies on Newton-Raphson (NR), Expectation-Maximization (EM), or Fisher algorithms for obtaining the final estimates, we implement matrix theories to circumvent the difficulties in the estimation process imposed by the inversion and the determinant of the variance-covariance matrix. Numerous simulations are conducted in evaluations of the proposed approach. For instance, in the study of the comparison between the proposed method and MLE, the former yields better estimates in the variance component with the compound symmetric covariance and presents remarkable improvements in estimating both the variance and the autocorrelation components in AR(1). In the study of investigating the model selection performance using the proposal estimation approach with the Schwarz Information Criterion (SIC) serving as the selection criterion, the simulation results demonstrate that the proposed approach to estimation performs effectively with a moderate amount of missing proportion reg (open full item for complete abstract)

Committee: Junfeng Shang Ph.D. (Advisor); Hanfeng Chen Ph.D. (Committee Member); John Chen Ph.D. (Committee Member); Jonathan Bostic Ph.D. (Other) Subjects: Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2020, Statistics

The analyses of correlated, repeated measures, or multilevel data with a Gaussian response are often based on models known as the linear mixed models (LMMs). LMMs are modeled using both fixed effects and random effects. The random intercepts (RI) and random intercepts and slopes (RIS) models are two exceptional cases from the linear mixed models that are taken into consideration. Our primary focus in this dissertation is to propose an approach for simultaneous selection and estimation of fixed effects only in LMMs. This dissertation, inspired by recent research of methods and criteria for model selection, aims to extend a variable selection procedure referred to as minimum approximated information criterion (MIC) of Su et al. (2018). Our contribution presents further use of the MIC for variable selection and sparse estimation in LMMs. Thus, we design a penalized log-likelihood procedure referred to as the minimum approximated information criterion for LMMs (lmmMAIC), which is used to find a parsimonious model that better generalizes data with a group structure. Our proposed lmmMAIC method enforces variable selection and sparse estimation simultaneously by adding a penalty term to the negative log-likelihood of the linear mixed model. The method differs from existing regularized methods mainly due to the penalty parameter and the penalty function. With regards to the penalty function, the lmmMAIC mimics the traditional Bayesian information criterion (BIC)-based best subset selection (BSS) method but requires a continuous or smooth approximation to the L0 norm penalty of BSS. In this context, lmmMAIC performs sparse estimation by optimizing an approximated information criterion, which substantially requires approximating that L0 norm penalty of BSS with a continuous unit dent function. A unit dent function, motivated by bump functions called mollifiers (Friedrichs, 1944), is an even continuous function with a [0, 1] range. Among several unit dent functions, inc (open full item for complete abstract)

Committee: Junfeng Shang Ph.D. (Advisor); Melissa Kary Miller Ph.D. (Other); Hanfeng Chen Ph.D. (Committee Member); Wei Ning Ph.D. (Committee Member) Subjects: Statistics

Master of Science, Miami University, 2025, Mechanical and Manufacturing Engineering

Reduced order modeling (ROM) methods, such as those based upon Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), offer data-based turbulence modeling with potential applications for flow control. While these models are often cheaper than numerical approaches, their results require validation with source data. Within the literature, the metrics and standards used to validate these models are often inconsistent. Chabot (2014) produced a data-driven framework for validating these ROMs that used surrogate Markov models (SMMs) to compare how the system dynamics evolved rather than how any single metric evolved. These SMMs were constructed by clustering the flow data into different states of suitably similar flow fields, and the Markov model then mapped how likely each state was to transition into another. While this method was successful, there persisted an amount of uncertainty in how the outlier states within this clustering scheme were determined. Additionally, the study only examined the application of this procedure to POD-Galerkin ROMs. This study aims to tie the outlier state determination directly to the models' parent data. The study will also apply this procedure to ROMs generated from DMD to investigate how this framework's effectiveness carries over to different classes of ROMs.

Committee: Edgar Caraballo (Advisor); Andrew Sommers (Committee Member); Mehdi Zanjani (Committee Member) Subjects: Aerospace Engineering; Fluid Dynamics; Mathematics; Mechanical Engineering; Statistics

Master of Science, The Ohio State University, 2008, Graduate School

Committee: Not Provided (Other) Subjects:

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2024, Biological Sciences

As human-modified landscape and climate changes proliferate, maintaining biodiversity and understanding the function and quality of available habitat is imperative. Anurans (frogs/toads) can be indicator species of habitat quality and ecosystem productivity, due to their permeable skin, small body size and ectothermy. We explored the relationship between Anurans and habitat quality by assessing the effects of spatial and temporal heterogeneity on the presence of Anurans. Across the Toledo Metropolitan Area (TMA), including the biodiversity hotspot Oak Openings Region (OOR), we surveyed across three years, 67 different wetland sites (N=1800). There was a difference in community assemblage between rural and suburban/urban habitats driven by factors related to human-modification (impervious surface), composition (landcover type) and productivity (e.g., NDVI). Areas with more impervious surface, lower amounts of swamp forest, and lower NDVI had fewer species. The differences in spatial structure but lack of differences in temporal variables among sites suggest spatial factors dominated. We also developed spatial models for predicting species richness across the region to evaluate spatial variables driving community composition and ecosystem productivity. The amount of cropland best predicted species richness, followed by amount of swamp forest. Among individual species, the most important variables differed; cropland (Acris blanchardi, Lithobates catesbeianus, Anaxyrus americanus, Anaxyrus fowleri and Hyla versicolor), floodplain forest (Lithobates clamitans), wet prairie (Lithobates pipiens), and swamp forest (Pseudacris crucifer, Pseudacris triseriata, Lithobates sylvaticus) were leading influences. Finally, we surveyed 304 local residents to assess their views on topics from support of new parks/preserves to fees to utilize parks, before a 25-minute presentation on Anurans, and resurveying them. There was strong support for many conservation-oriented questions, but (open full item for complete abstract)

Committee: Karen Root Ph.D. (Advisor); Paul Moore Ph.D. (Committee Member); Ashley Ajemigbitse Ph.D. (Other); Jeffrey Miner Ph.D. (Committee Member); Helen Michaels Ph.D. (Committee Member) Subjects: Biology; Conservation; Ecology; Wildlife Conservation; Wildlife Management

PhD, University of Cincinnati, 2022, Business: Business Administration

High-dimensional data analysis has played an essential role in modern scientific discoveries. Identifying important predictors among many candidate features is a challenging yet crucial problem. This dissertation consists of two essays that study the inference for high-dimensional linear models and the distress risk prediction in finance. Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to quantify. A critical question remains unsettled; that is, how to embed the model selection uncertainty into a simultaneous inference of the model coefficients? Is it even possible? In Essay I, we propose a new type of simultaneous confidence intervals --- sparsified simultaneous confidence intervals. Our intervals divide the covariates into three groups --- unimportant, plausible, and significant covariates --- offering more insights about the true model. Specifically, the upper and lower bounds of the intervals of the unimportant covariates are shrunken to zero (i.e., [0,0]), meaning these covariates should be excluded from the final model, while the intervals of plausible or significant covariates are either containing zero (e.g., [-1,1] or [0,1]) or not containing zero (e.g., [2,3]). The proposed method can be coupled with various selection procedures, making it ideal for comparing their uncertainty. We establish desirable asymptotic properties for the proposed method, develop intuitive graphical tools for visualization, and justify its superior performance through simulation and real data analysis. Essay II studies distress risk prediction, which is vitally important for risk management and asset pricing. In this Essay, we distinguish two types of events of financial distress, bankruptcy and delisting due to other failures, for the first time. They are two closely related yet sharply different distress events. Using a state-of-the-art adaptive Lasso (open full item for complete abstract)

Committee: Yan Yu Ph.D. (Committee Member); Chen Xue Ph.D. (Committee Member); Yichen Qin Ph.D. (Committee Member); Dungang Liu Ph.D. (Committee Member) Subjects: Statistics

Master of Science (MS), Bowling Green State University, 2022, Applied Statistics (Math)

One of the most important features of collected data is the identification of change points. Researchers are often tasked with identifying abrupt or any changes that appeared in a dataset. Identifying these changes and extracting meaningful information is very important to benefit and avoid losses. In the early 1970's Hirotugu Akaike formulated what is now called the Akaike Information Criterion (AIC). After that, in 1978, Schwarz introduced the improved version of the AIC called Schwarz Information Criterion (SIC) which served as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. In this thesis, statistical analysis of regression models related to the application of modified information criterion (MIC) introduced by Chen et al (2006) will be explored along with the comparison of SIC. Chapters 2 and 3 consists of the derivations of theoretical foundation and mathematical formulae. The regression model is employed in each situation. Simulations have been conducted for each information criterion to compare the performance of the two approaches. After the comparison of the performances, the application of the MIC has been employed on three different datasets out of which two have already been tested for finding the change point locations. The only difference between these two information criteria is in their penalty terms. The objective of the thesis is to compare the performance of these two approaches and use the better one to extract meaningful information after the identification of change point locations.

Committee: Wei Ning Ph.D. (Committee Chair); John Chen Ph.D. (Committee Member) Subjects: Mathematics; Statistics

Doctor of Philosophy, Miami University, 0, Psychology

General Recognition Theory (GRT; Ashby & Townsend, 1986) is a theoretical framework for analyzing the perceptual and decisional processing of multidimensional stimuli. In-depth applications of GRT involve hierarchical modeling of the underlying perceptual distributions covering the theoretical decisional space. However, these models are not identifiable in the most fundamental GRT experimental design, the 2x2 feature-complete factorial design. The present work introduces the idea of mean-variance relationships into the GRT framework to address this degrees of freedom problem. This dissertation was separated into three sections. Section 1 focuses on establishing mean-variance relationships in perceptual and decisional processing and argues for the relevance of this concept in the GRT context. Key results include a rigorous definition for mean-variance relationships in GRT models and a specification of the form these relationships are expected to take (a power-law). Section 2 introduces two models into signal detection theory (SDT), the one-dimensional version of GRT. These models use the Poisson and Gamma distributions to exhibit mean-variance relationships. Keys results include the detailing of properties of these models important for GRT, a method for fitting these models using generalized linear models, and a demonstration of non-identifiability in one-interval designs. Section 3 expands the Poisson and Gamma SDT models into the GRT context and connects them to standard GRT concepts. Key results include a method to fit these models using vector generalized linear models (Yee, 2015) and a demonstration of the superior performance of these models on historical datasets.

Committee: Joseph Houpt (Committee Member); Seonjin Kim (Committee Member); Robin Thomas (Committee Chair); Joseph Johnson (Committee Member) Subjects: Cognitive Psychology

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2021, Statistics

High-dimensional data are widely encountered in a great variety of areas such as bioinformatics, medicine, marketing, and finance over the past few decades. The curse of high-dimensionality presents a challenge in both methodological and computational aspects. Many traditional statistical modeling techniques perform well for low-dimensional data, but their performance begin to deteriorate when being extended to high-dimensional data. Among all modeling techniques, variable selection plays a fundamental role in high-dimensional data modeling. To deal with the high-dimensionality problem, a large amount of variable selection approaches based on regularization have been developed, including but not limited to LASSO (Tibshirani, 1996), SCAD (Fan and Li, 2001), Dantzig selector (Candes and Tao, 2007). However, as the dimensionality getting higher and higher, those regularization approaches may not perform well due to the simultaneous challenges in computational expediency, statistical accuracy, and algorithm stability (Fan et al., 2009). To address those challenges, a series of feature screening procedures have been proposed. Sure independence screening (SIS) is a well-known procedure for variable selection in linear models with high and ultrahigh dimensional data based on the Pearson correlation (Fan and Lv, 2008). Yet, the original SIS procedure mainly focused on linear models with the continuous response variable. Fan and Song (2010) also extended this method to generalized linear models by ranking the maximum marginal likelihood estimator (MMLE) or maximum marginal likelihood itself. In this dissertation, we consider extending the SIS procedure to high-dimensional generalized linear models with binary response variable. We propose a two-stage feature screening procedure for generalized linear models with a binary response based on point-biserial correlation. The point-biserial correlation is an estimate of the correlation between one continuous variable and (open full item for complete abstract)

Committee: Junfeng Shang (Committee Chair); Emily Freeman Brown (Committee Member); Hanfeng Chen (Committee Member); Wei Ning (Committee Member) Subjects: Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2021, Mathematics/Mathematical Statistics

Bootstrap is a widely applicable computational statistical method and introduced by Efron (1979). The idea of bootstrap has extended to linear mixed models (LMMs) and is well established for the LMMs with homoscedasticity assumption. Thus, our specific focus in this dissertation lies on developing a bootstrap method for LMMs under homoscedasticity violation (heteroscedasticity). In the study, we assume that the form of heteroscedasticity is unknown. Thus, to generate bootstrap response data as close as possible to the actual response data, we obtain the marginal residuals and transform them to ensure that the variance of the modified marginal residuals is an unbiased estimator of the variance of the error terms. The idea of the proposed bootstrap is inspired by Wu (1986). Furthermore, we prove the consistency of the bootstrap procedure, which demonstrates that the proposed bootstrap method has asymptotically valid inferences in the estimation of parameters in LMMs. Simulations are conducted under different scenarios by varying error covariance structures and sample sizes. We generate data with four covariance structures and three sample size settings. Moreover, to show the effectiveness of the proposed method over the other methods, we compare the results of the proposed method with existing bootstrap methods: parametric, residual, REB, and wild. By considering the above scenarios, we carry out a series of simulations under five different objectives. In the first two objectives, we observe the bootstrap distributions of model coefficients and set out the number of bootstrap replications as suitable for the upcoming simulations. In the third and fourth objectives, we study the parameter estimation performance and assess parameter estimation accuracy. Finally, we compute the empirical coverage probability of the parameters. The simulation results with the heteroscedastic errors demonstrate that the accuracy of the estimation process of the proposed bootstr (open full item for complete abstract)

Committee: Junfeng Shang Ph.D. (Advisor); Hanfeng Chen Ph.D. (Committee Member); Wei Ning Ph.D. (Committee Member); Hrishikesh Joshi Ph.D. (Other) Subjects: Statistics

PhD, University of Cincinnati, 2021, Business: Business Administration

This dissertation is motivated by the problem of crowding in the emergency department. A near-universal problem, crowding has been linked to negative outcomes for both patients and providers. A primary cause of crowding is the inherent stochasticity of patient arrivals. Stochasticity, while operationally problematic, is difficult to control in an emergency department where all patients seeking care must be seen. As it cannot be eliminated, accounting for stochasticity is critical to mitigating crowding in the emergency department. Because both crowding and its consequences occur in real time, any analytical model designed to support operational decisions must also provide insights in real time. A review of the literature reveals that, while many arrival forecasting models have been proposed, few have been assessed for their ability to support real-time decision-making during demand surges. This dissertation studies the design of such models with an eye towards operational support, such as the activation of backup staff when beneficial. Using a unique set of data --- made up of approximately 875,000 patient encounters from four hospitals across two health systems --- valuable insights as to the importance of distributional assumptions when forecasting during demand surges are identified. Namely, when quantifying the risk of a potential crowding event, discrete distributional forecasts (e.g., those with Poisson and Negative Binomial predictive distributions) will outperform typical Gaussian-based models. In addition, it is shown that proactive activation of backup staff, based on an appropriately constructed model, can lead to decreased patient waiting times compared to typical current practice. Importantly, this benefit to patients comes at a cost to schedule stability for providers. Intelligent management of this tradeoff presents opportunities for both improvements to practice and future research.

Committee: Craig Froehle Ph.D. (Committee Chair); Jeffrey Mills Ph.D. (Committee Member); Yichen Qin (Committee Member); Uday Rao Ph.D. (Committee Member) Subjects: Health Care

Master of Science, University of Toledo, 2009, Civil Engineering

Prediction of future pavement conditions is one of the important functions of pavement management systems. They are helpful in determining the rate of roadway network deterioration both at the network-level and project-level management, which forms a major part of engineering decision making and reporting. Network-level management focuses on determination and allocation of funds to maintain the pavement network above a specified operational standard and does not give importance to how the individual pavement sections deteriorate. Therefore, a survival time analysis is determined to predict the remaining service life. At the project-level, engineers make decisions on which pavement to repair, when and how to repair. Therefore, it requires more condition accuracy than network-level. The two adjustment methods proposed by Shahin (1994) and Cook and Kazakov (1987) are often used to obtain more condition prediction at the project-level. Both the Shahin and the Cook and Kazakov models take into account a family average curve in predicting deterioration of individual pavement sections. This prediction is done through the latest available condition-age point of an individual pavement section and does not consider all available data points. This study considers the most commonly used pavement condition prediction models viz. linear regression, polynomial constrained least squares, S-shape and power curve. The prediction accuracy of these four models is compared. Further the prediction accuracy of each of the four models is compared with their respective the Shahin's and the Cook's models to determine whether is it possible to further improve the prediction accuracy error for each of the four models.

Committee: Eddie Y. Chou PhD (Committee Chair); George J. Murnen PhD (Committee Member); Andrew G. Heydinger PhD (Committee Member) Subjects: Civil Engineering; Engineering; Transportation

Master of Science, The Ohio State University, 2019, Environment and Natural Resources

Oak (Quercus spp.) and hickory (Carya spp.) trees are failing to replace themselves in forests of the eastern U.S., likely due to fire suppression and a moister climate during the past century. Our study explored the implications of this mesophication process for future forest composition in southeastern Ohio. In 2016-2018 we resampled permanent plots first established in 1993-1995, in mature forests of the Athens and Marietta Units of the Wayne National Forest. We used mixed logistic regression models to characterize mortality patterns of five oak and one hickory species, and generalized linear mixed models to characterize sapling density patterns of three common shade-tolerant tree species that are likely to dominate future forest composition. For both the mortality and sapling models, we chose a set of a priori topographic, edaphic, and stand structural variables, and used the full set of a priori covariates for analysis of each species. Our mortality data revealed relatively high mortality rates for all species of the red oak subgenus (Erythrobalanus). Models indicated that chestnut oak (Quercus montana) and pignut hickory (Carya glabra) mortality were positively associated with competition, while white oak (Quercus alba) mortality was negatively associated with competition. Northern red oak (Quercus rubra) mortality was associated with mesic topographic positions and older stand age. Our sapling data showed that American beech (Fagus grandifolia) nearly doubled in density between the two sampling periods (217 trees per hectare[tph] 1990s, 429 tph 2010s), while both red maple (Acer rubrum) and sugar maple (Acer saccharum) nearly halved in density (red maple 441 tph 1990s, 216 tph 2010s; sugar maple 608 tph 1990s, 298 tph 2010s). Models indicated that soil acidity was positively related with red maple sapling density, and negatively associated with sugar maple sapling density. Higher slope positions were positively related with red maple sapling density (open full item for complete abstract)

Committee: Stephen Matthews N. (Advisor); David Hix M. (Advisor); Sayeed Mehmood R. (Committee Member); Gabriel Karns R. (Committee Member) Subjects: Ecology; Environmental Science; Forestry

Doctor of Philosophy, University of Akron, 2018, Mechanical Engineering

Cars' auto auctions generally face a specific regression in the profits due to the unfortunate decision-making of auctioning cars without any prior research. This paper examines the possibility of increasing the profits of a particular cars' auto auction located in New England, Connecticut. Based on the collected data from the auction this study aims to predict the selling probability of cars and their selling prices; thus, increase its profits through the application of data mining techniques and utilization of multiple predictive models. Three classifiers were applied to predict the selling probability of cars; logistic regression, decision tree, and neural network which were later incorporated to produce three scenarios that would increase the accuracy of predictions and consequently ensure their effectiveness, whereas the multiple linear regression was administrated to predict the cars' selling prices. Subsequently, an agent-based model was built to produce a simulation that adequately represents the results of this research in reality and create a model ready to operate under any suitable data, which would serve many auto auctions besides the one upon which this study is based. By comparing the baseline and predicted profit, this study concludes the effectiveness of its methods in raising the profit of the auto auction where the highest increment by the models is 19.49%. This study has several recommendations for future examination. Further research could be conducted to identify interested buyers, their exact percentage and based on determining the buying trends of the interested buyers if a car is predicted as sold in the model but was not, further studies could investigate the expected time of its selling or if it will be sold at all.

Committee: Shengyong Wang Dr. (Advisor); Yilmaz Sozer Dr. (Committee Member); Sergio Felicelli Dr. (Committee Member); Ling Chen Dr. (Committee Member); Nao Mimoto Dr. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2017, Business: Business Administration

In the electric utility industry, it could be challenging to adjust supply to match demand due to large generator ramp up times, high generation costs and insufficient in-house generation capacity. Demand response (DR) is a technique for adjusting the demand for electric power instead of the supply. Direct Load Control (DLC) is one of the ways to implement DR. DLC program participants sign up for power interruption contracts and are given financial incentives for curtailing electricity usage during peak demand time periods. This dissertation studies a DLC program for residential air conditioners using mathematical optimization models. First, we develop a model that determines what contract parameters to use in designing contracts between the provider and residential customers, when to turn which power unit on or off and how much power to cut during peak demand hours. The model uses information on customer preferences for choice of contract parameters such as DLC financial incentives and energy usage curtailment. In numerical experiments, the proposed model leads to projected cost savings of the order of 20%, compared to a current benchmark model used in practice. We also quantify the impact of factors leading to cost savings and study characteristics of customers picked by different contracts. Second, we study a DLC program in a macro economic environment using a Computable General Equilibrium (CGE) model. A CGE model is used to study the impact of external factors such as policy and technology changes on different economic sectors. Here we differentiate customers based on their preference for DLC programs by using different values for price elasticity of demand for electricity commodity. Consequently, DLC program customers could substitute demand for electricity commodity with other commodities such as transportation sector. Price elasticity of demand is calculated using a novel methodology that incorporates customer preferences for DLC contracts from the first m (open full item for complete abstract)

Committee: Uday Rao Ph.D. (Committee Chair); Debashis Pal Ph.D. (Committee Member); R. Kenneth Skinner Ph.D. (Committee Member); Yan Yu Ph.D. (Committee Member); Jeffrey Camm Ph.D. (Committee Member) Subjects: Operations Research

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2017, Mathematics/Mathematical Statistics

A linear mixed model is a useful technique to explain observations by regarding them as realizations of random variables, especially when repeated measurements are made to statistical units, such as longitudinal data. However, in practice, there are often too many potential factors considered affecting the observations, while actually, they are not. Therefore, statisticians have been trying to select significant factors out of all the potential factors, where we call the process model selection. Among those approaches for linear mixed model selection, penalized methods have been developed profoundly over the last several decades. In this dissertation, to solve the overfitting problem in most penalized methods and improve the selection accuracy, we mainly focus on a penalized approach via cross-validation. Unlike the existing methods using the whole data to fit and select models, we split the fitting process and selection into two stages. More specifically, an adaptive lasso penalized function is customized in the first stage and marginal BIC criterion is used in the second stage. We consider that the main advantage of our approach is to reduce the dependency between models construction and evaluation. Because of the complex structure of mixed models, we adopt a modified Cholesky decomposition to reparameterize the model, which in turn significantly reduces the dimension of the penalized function. Additionally, since random effects are missing, there is no closed form for the maximizer of the penalized function, thus we implement EM algorithm to obtain a full inference of parameters. Furthermore, due to the computation limit and moderately small samples in practice, some noisy factors may still remain in the model, which is particularly obvious for fixed effects. To eliminate the noisy factors, a likelihood ratio test is employed to screen the fixed effects. Regarding the overall process, we call it adaptive lasso via cross-validation. Additionally, we dem (open full item for complete abstract)

Committee: Junfeng Shang (Advisor); Angela Thomas (Other); Hanfeng Chen (Committee Member); John Chen (Committee Member) Subjects: Statistics

Master of Science, The Ohio State University, 2017, Mechanical Engineering

Recently Krak and Singh (Mech. Syst. Signal Process., 84(A), 598-614, 2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. The major goal of this thesis is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

Committee: Rajendra Singh PhD (Advisor); Jason Dreyer PhD (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2016, Statistics

Linear mixed models describe the relationship between a response variable and some predictors for data that are grouped according to one or more clustering factors. A linear mixed model consists of both fixed effects and random effects. Fixed effects are the conventional linear regression coefficients, and random effects are associated with units which are drawn randomly from a population. By accommodating such two types of parameters, linear mixed models provide an effective and flexible way of representing the means as well as the covariance structure of the data, therefore have been primarily used to model correlated data, and have received much attention in a variety of disciplines including agriculture, biology, medicine, and sociology. Due to the complex nature of the linear mixed models, the selection of only important covariates to create an interpretable model becomes challenging as the dimension of fixed or random effects increases. Thus, determining an appropriate structural form for a model to be used in making inferences and predictions is a fundamental problem in the analysis of longitudinal or clustered data using linear mixed models. This dissertation focuses on selection and estimation for linear mixed models by integrating the recent advances in model selection. More specifically, we propose a two-stage penalized procedure for selecting and estimating important fixed and random effects. Compared with the traditional subset selection approaches, penalized methods can enhance the predictive power of a model, and can significantly reduce computational cost when the number of variables is large (Fan and Li, 2001). Our proposed procedure is different from the existing ones in the literature mainly in two aspects. First, the proposed method is composed of two stages to separately choose the parameters of interests, therefore can respect and accommodate the distinct properties between the random and fixed effects. Second, the usage of the profil (open full item for complete abstract)

Committee: Junfeng Shang (Advisor); Lewis Fulcher (Other); Hanfeng Chen (Committee Member); John Chen (Committee Member) Subjects: Statistics

Doctor of Philosophy, University of Toledo, 2015, Mathematics (statistics)

First, we propose a two-step estimation method for periodic autoregressive parameters via residuals when the observations contain trend and periodic autoregressive time series. In the first step, the trend is estimated and the residuals are calculated; in the second step, the autoregressive coefficients are estimated from the residuals. To overcome the drawback of a parametric trend estimation, we estimate the trend nonparametrically by polynomial spline smoothing. Polynomial spline smoothing is one of the nonparametric methods commonly used in practice for function estimation. It does not require any assumption about the shape of the unknown function. In addition, it has advantages of computational expediency and mathematical simplicity. The oracle efficiency of the proposed Yule-Walker type estimator is established. The performance is illustrated by simulation studies and real data analysis. Second, we consider time series that contain a trend, a seasonal component and periodically correlated time series. A semiparametric three-step method is proposed to analyze such time series. The seasonal component and trend are estimated by means of B-splines, and the Yule-Walker estimates of the time series model coefficients are calculated via the residuals after removing the estimated seasonality and trend. The oracle efficiency of the proposed Yule-Walker type estimators is established. Simulation studies suggest that the performance of the estimators coincides with the theoretical results. The proposed method is applied to three data sets. Third, we will make the inference for the logistic regression models using the nonparametric estimation method. The primary interest of this topic is the estimation of the conditional mean for the logistic regression models. We propose the local likelihood logit method with linear B-spline to estimate the conditional mean. Simulation studies shows that our method works well.

Committee: Qin Shao (Committee Chair); Donald White (Committee Member); Rong Liu (Committee Member); Jing Wang (Committee Member) Subjects: Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2014, Mathematics/Mathematical Statistics

Model selection plays an important role in statistical literature. The objective of model selection is to choose the most appropriate model from a potential large class of candidate models that balance the increase in fit against the increment in model complexity. To facilitate the selection process, a variety of model selection criteria are employed and have been developed for optimal selection of the most appropriate model. The most popular model selection criteria are the Akaike Information Criterion (AIC, 1973. 1974) and the Bayesian Information Criterion (BIC, 1976). Over the past several decades, a number of additional model selection criteria have been proposed and investigated. One important one among these is Cp from Mallow (1973), which is based on the Gauss discrepancy. In the dissertation, we focus on the development of variants of Cp in linear mixed models. Linear mixed model theory has expanded greatly in recent years, resulting in its widespread application in many areas of research. Therefore, the improvement of Cp in linear mixed model setting will significantly increase the efficiency and effectiveness of model selection. We propose the model selection criteria following Mallow's Cp (1973) statistic in linear mixed models. The first proposed criterion is marginal Cp, called MCp. We first derive MCp based on the expected Gauss discrepancy. For the set of candidate models including the true model, we adopt a consistent estimator of correlation matrix of response data. Then we form and prove an idempotent matrix in linear mixed models, which leads to an asymptotically unbiased estimator of the expected Gauss discrepancy between a candidate model and the true model, called MCp. An improvement of MCp, called IMCp, is then proposed and proved, which is also an asymptotically unbiased estimator of the expected Gauss discrepancy. In the simulation study, a set of increasing correlation coefficients in the correlation matrix of the response (open full item for complete abstract)

Committee: Junfeng Shang (Advisor); Hanfeng Chen (Committee Member); John Chen (Committee Member); Alexander Goberman (Committee Member) Subjects: Statistics