Doctor of Philosophy, The Ohio State University, 2005, Statistics

As more and more dense, yet cost-effective, genetic maps become increasingly available, the focus of linkage analysis is shifting from testing for linkage signals to sufficiently localizing putative disease loci before fine mapping begins. Currently, there exists only a limited number of methods that provide confidence regions for the locations of trait loci. Among them is the confidence set inference (CSI) procedure based on the mean IBD sharing statistic for data from affected sib-pair studies described by Lin (2002) that deduces such regions with known lower bound on their coverage. Although this method has many attractive features, including avoidance of multiplicity adjustment for the number of markers scanned, its formulation poses some restrictions that limit its usefulness on practical applications. First, it assumes that all markers are 100% polymorphic, so that the IBD state at each of them is inferred unequivocally, an assumption rarely met in reality. Second, when the genetic map available is sparse, it tends to produce intervals that overcover the trait locus. Finally, its application requires knowledge of the IBD sharing distribution at the trait locus by an affected sib-pair. These probabilities are estimated using population disease characteristics that can be obtained through epidemiological studies with reasonable accuracy. However, there is a number of issues that renders this method of estimating the IBD distribution impractical. We propose several extensions that address some of the limitations of the CSI approach. First, we extend it to accommodate markers with incomplete polymorphism, thereby increasing its practical value. Next, we modify it so that it tests each location on the genome for its possibility to be the trait locus. This way, we obtain regions with known exact coverage probability, rather than placing a lower bound on it. Finally, a two-step application of the CSI approach promises to avoid using population disease characteristics (open full item for complete abstract)

Committee: Shili Lin (Advisor) Subjects:

Master of Science in Civil Engineering, Cleveland State University, 2012, Fenn College of Engineering

This work presents the mathematical constructs for certain statistical elements that when combined properly produce a quality control program that can be used to accept or reject ceramic materials based on mechanistic strength information. Due to the high tensile strength and low fracture toughness of ceramic materials the design engineer must consider a stochastic design approach. Critical flaws with lengths that cannot be detected by current non-destructive evaluation methods render a distribution of defects in ceramics that effectively requires that the tensile strength of the material must be treated as a random variable. The two parameter Weibull distribution (an extreme value distribution) with size scaling is adopted for tensile strength in this work. Typically the associated Weibull distribution parameters are characterized through the use of four-point flexure tests. The failure data from these tests are used to determine the Weibull modulus (m) and a Weibull characteristic strength (σθ). To determine an estimate of the true Weibull distribution parameters maximum likelihood estimators are used. The quality of the estimated parameters relative to the true distribution parameters depends fundamentally on the number of samples taken to failure and the component under design. The statistical concepts of “confidence intervals” and “hypothesis testing” are discussed here relative to their use in assessing the “goodness” of the estimated distribution parameters. Both of these inferential statistics tools enable the calculation of likelihood confidence rings. Work showing how the true distribution parameters lie within a likelihood ring with a specified confidence is presented. A material acceptance criterion is defined here and the criterion depends on establishing an acceptable probability of failure of the component under design as well as an acceptable level of confidence associated with estimated distribution parameter determined using failure data from a (open full item for complete abstract)

Committee: Stephen Duffy PhD (Committee Chair); Lutful Khan PhD (Committee Member); Jacqueline Jenkins PhD (Committee Member) Subjects: Civil Engineering

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

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

Many studies deal with inflated and nonnegative data, such as in medical studies. Most studies that deal with inflated data deal with zero-inflated datasets, but there are many datasets that are zero-one inflated as well. Zero-inflated datasets are characterized by a significant proportion of zero values, leading to a skewed distribution. Zero-One inflated datasets are characterized by a significant proportion of zero and one values, which also leads to a skewed distribution. It is common practice to use the Central Limit Theorem to assume an approximately normal distribution to construct confidence intervals and conduct hypothesis tests. However with inflated and highly skewed distributions, this practice leads to an inaccurate result. The empirical likelihood method offers an alternative method of computing confidence intervals with the benefit of having no distributional assumptions. Although the empirical likelihood method provides an improvement, it suffers from several drawbacks. In this dissertation, we propose several modified empirical likelihood methods to combat these drawbacks. We use these modified methods, along with the empirical likelihood and normal approximation methods, to construct confidence intervals based on zero-inflated data and zero-one inflated data. We compare the performance of each method for these two situations on both simulated data and real data. Furthermore, we develop a hypothesis test for comparing two means based on one of the modified empirical likelihood approaches. We then test the modified empirical likelihood approach against the empirical likelihood and normal approximation methods using simulated and real data.

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

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

Distance correlation is a measure of the relationship between random vectors in arbitrary dimension. A sample distance covariance can be formulated in both an unbiased estimator and a biased estimator of distance covariance, where distance correlation is defined as the normalized coefficient of distance covariance. The jackknife empirical likelihood for a U-statistic by Jing, Yuan, and Zhou (2009) can be applied to a distance correlation since the empirical likelihood method fails in nonlinear statistics. A Wilks' theorem for jackknife empirical likelihood is shown to hold for distance correlation. This research shows how to construct a confidence interval for distance correlation based on jackknife empirical likelihood for a U-statistic, where the sample distance covariance can be represented as a U-statistic. In comparing coverage probabilities of confidence intervals for distance correlation based on jackknife empirical likelihood and bootstrap method, coverage probabilities for the jackknife empirical likelihood show more accuracy. We propose the estimation and the visualization of local distance correlation by using a local version of the jackknife empirical likelihood. The kernel density functional estimation is used to construct the jackknife empirical likelihood locally. The bandwidth selection for kernel function should minimize the distance between the true density and estimated density. Local distance correlation has the property that it equals zero in the neighborhood of each point if and only if the two variables are independent in that neighborhood. The estimation and visualization of local distance correlation are shown as accurate to capture the local dependence when compared with the local Gaussian correlation in simulation studies and real examples.

Committee: Maria Rizzo Ph.D. (Advisor); Jari Willing Ph.D. (Other); Wei Ning Ph.D. (Committee Member); Junfeng Shang Ph.D. (Committee Member) Subjects: Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2018, Mathematics/Mathematical Statistics

Generalizations of univariate distributions are often of interest to serve for real life phenomena. These generalized distributions are very useful in many ¿elds such as medicine, physics, engineer-ing and biology. Lomax distribution (Pareto-II) is one of the well known univariate distributions that is considered as an alternative to the exponential, gamma, and Weibull distributions for heavy tailed data. However, this distribution does not grant great ¿exibility in modeling data. In this dissertation, we introduce a generalization of the Lomax distribution called Rayleigh Lo-max (RL) distribution using the form obtained by El-Bassiouny et al. (2015). This distribution provides great ¿t in modeling wide range of real data sets. It is a very ¿exible distribution that is related to some of the useful univariate distributions such as exponential, Weibull and Rayleigh dis-tributions. Moreover, this new distribution can also be transformed to a lifetime distribution which is applicable in many situations. For example, we obtain the inverse estimation and con¿dence intervals in the case of progressively Type-II right censored situation. We also apply Schwartz information approach (SIC) and modi¿ed information approach (MIC) to detect the changes in parameters of the RL distribution. The performance of these approaches is studied through simu-lations and applications to real data sets. According to Aryal and Tsokos (2009), most of the real world phenomenon that we need to study are asymmetrical, and the normal model is not a good model for studying this type of dataset. Thus, skewed models are necessary for modeling and ¿tting asymmetrical datasets. Azzalini (1985) in-troduced the univariate skew normal distribution and his approach can be applied in any symmet-rical model. However, if the underlying (base) probability is not symmetric, we can not apply the Azzalini's approach. This motivated the study for more ¿exible alternative. Shaw and Buckley (2007) introduced a q (open full item for complete abstract)

Committee: Arjun Gupta Ph. D. (Committee Co-Chair); Wei Ning Ph. D. (Committee Co-Chair); John Chen Ph. D. (Committee Member); Jane Chang Ph. D. (Other) Subjects: Statistics

PhD, University of Cincinnati, 2005, Arts and Sciences : Mathematical Sciences

Several statistical methods, used to construct confidence intervals (CIs) for a single Binomial proportion, are selected based on literature recommendations and are compared. A new criterion ‘strict nesting condition' is defined when comparing different confidence interval methods. The focus is on Blaker's method and its potential shortness in practice is discussed. The continuity correction and smoothing technique are proposed to improve Blaker's method. The fundamental confidence interval obtained from a fundamentally defined p-value is also introduced and compared with the Blaker's and Clopper-Pearson's (C-P's) methods. The continuity correction (CC) and smoothing technique can also be used to improve the fundamental method. The modified fundamental method and Blaker's method have great similarities in term of coverage, length, confidence curve shape, etc. The power behaviors in modified CC Blaker's and fundamental methods are examined and compared with C-P's. For two sample proportion inference, the three existing exact confidence interval methods that are available in StatXact are discussed and compared for the difference of 2 Binomial proportions. A simple approach based on the one sample exact methods is introduced to obtain the exact confidence interval of the difference when data are balanced. Its performance is comparable to these existing methods but the computation is much simpler.

Committee: Dr. James Deddens (Advisor) Subjects: Mathematics; Statistics

Doctor of Philosophy, The Ohio State University, 2012, Nuclear Engineering

Utilities operating nuclear power plants in the United States are required to demonstrate that their plants comply with the safety requirements set by the U.S. Nuclear Regulatory Commission (NRC). How to show adherence to these limits through the use of computer code surrogates is not always straightforward, and different techniques have been proposed and approved by the regulator. The issue of compliance with regulatory limits is examined by rephrasing the problem in terms of hypothesis testing. By using this more rigorous framework, guidance is proposed to choose techniques to increase the probability of arriving at the correct conclusion of the analysis. The findings of this study show that the most straightforward way to achieve this goal is to reduce the variance of the output result of the computer code experiments. By analyzing different variance reduction techniques, and different methods of satisfying the NRC's requirements, recommendations can be made about the best-practices, that would result in a more accurate and precise result. This study began with an investigation into the point estimate of the 0.95-quantile using traditional sampling methods, and new orthogonal designs. From there, new work on how to establish confidence intervals for the outputs of experiments designed using variance reduction techniques was compared to current, regulator-approved methods. Lastly, a more direct interpretation of the regulator's probability requirement was used, and confidence intervals were established for the probability of exceeding a safety limit. From there, efforts were made at combining methods, in order to take advantage of positive aspects of different techniques. The results of this analysis show that these variance reduction techniques can provide a more accurate and precise result compared to current methods. This means an increased probability of arriving at the correct conclusion, and a more accurate characterization of the risk associated with even (open full item for complete abstract)

Committee: Tunc Aldemir PhD (Advisor); Richard Denning PhD (Committee Member); Marvin Nakayama PhD (Committee Member); Alper Yilmaz PhD (Committee Member) Subjects: Nuclear Engineering; Statistics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2009, Mathematics/Probability and Statistics

Multiple comparison inference is simultaneous inference ona comparison of the treatment means. The focus of this research was to develop simultaneous confidence interval methods for different types of multiple comparison inference when the equality of variances can not be assumed and when prior knowledge of the ratios of variance is available. Under the usual normality and equal variance assumptions, Dunnet's (1955) method provided the simultaneous inference on the difference between each new treatment mean and the control mean, which is useful for estimating the minimum effective dose (MED) and the maximum safe dose (MSD) in does-response studies. In practice, however, homogeneity of variances is seldom satisfied. In this research, an exact method for multiple comparisons with a control was developed when prior knowledge of the ratios of variance among treatments is available but without equal variance assumption. An example was considered and a simulation study on error rate was conducted. The results indicated that Dunnet's method has inflated error rate and may lead to erroneous inference when the equal variance assumption is not satisfied. In addition, robustness of the exact method was also examined through a simulation study. Tamhane and Logan (2003) proposed a simultaneous confidence interval method for identifying the MED and MSD, while assuming equal variance. By the same motivation, a method was proposed for identifying the doses which are both effective and safe when the variances are different among treatments and the ratios of variance are known. We suggested a simulation based approach to estimate the critical values. The power of the approach was estimated using a simulation study. In addition, all-pairwise comparisons are of interest in many circumstances. Under the unbalanced design, the Tukey-Kramer method provided a set of conservative simultaneous confidence intervals for all-pairwise differences assuming equal variances and normal distr (open full item for complete abstract)

Committee: Wei Ning (Committee Chair); Henfeng Chen (Committee Member); James Albert (Committee Member); Madhu Rao (Committee Member) Subjects: Statistics