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Ultra-high Dimensional Semiparametric Longitudinal Data Analysis

Green, Brittany
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1593171378846243

Abstract Details

2020, PhD, University of Cincinnati, Business: Business Administration.
As ultra-high dimensional longitudinal data is becoming ever more apparent in fields such as public health, information systems, and bioinformatics, developing flexible methods with a sparse set of important variables is of high interest. In this setting, the dimension of the covariates can potentially grow exponentially with respect to the number of clusters. This dissertation research considers a flexible semiparametric approach, namely, partially linear single-index models, for ultra-high dimensional longitudinal data. Most importantly, we allow not only the partially linear covariates, but also the single-index covariates within the unknown flexible function estimated nonparametrically to be ultra-high dimensional. Using penalized generalized estimating equations, this approach can capture correlation within subjects, can perform simultaneous variable selection and estimation with a smoothly clipped absolute deviation penalty, and can capture nonlinearity and potentially some interactions among predictors. We establish asymptotic theory for the estimators including the oracle property in ultra-high dimension for both the partially linear and nonparametric components. An efficient algorithm is presented to handle the computational challenges, and we show the effectiveness of our method and algorithm via a simulation study and yeast cell cycle gene expression data. In addition, we develop an alternative solution methodology via the penalized quadratic inference function with partially linear single-index models for ultra-high dimensional longitudinal data. This methodology can improve the estimation efficiency when the working correlation structure is misspecified. Performance is demonstrated via a simulation study and analysis of a genomic dataset.
Peng Wang, Ph.D. (Committee Chair)
Yan Yu, Ph.D. (Committee Chair)
Lenisa Chang, Ph.D. (Committee Member)
Business Administration
Single-index model; Generalized estimating equations; Polynomial spline; Variable selection

Recommended Citations

Citations

  • Green, B. (2020). Ultra-high Dimensional Semiparametric Longitudinal Data Analysis [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1593171378846243

    APA Style (7th edition)

  • Green, Brittany. Ultra-high Dimensional Semiparametric Longitudinal Data Analysis. 2020. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1593171378846243.

    MLA Style (8th edition)

  • Green, Brittany. "Ultra-high Dimensional Semiparametric Longitudinal Data Analysis." Doctoral dissertation, University of Cincinnati, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1593171378846243

    Chicago Manual of Style (17th edition)

ucin1593171378846243
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© 2020, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.