The rise of studies with high-dimensional potential covariates has invited a renewed interest in dimension reduction that promotes more parsimonious models, ease of interpretation and computational tractability. However, current variable selection methods restricted to continuous response often assume Gaussian response for methodological as well as theoretical developments. In this thesis, we consider regression models that induce sparsity, gain prediction power, and accommodates response distributions beyond Gaussian with common variance. The first part of this thesis is a transform-both-side Bayesian variable selection model (TBS) which allows skewness, heteroscedasticity and extreme heavy tailed responses. Our method develops a framework which facilitates computationally feasible inference in spite of inducing non-local priors on the original regression coefficients. Even if the transformed conditional mean is no longer linear with respect to covariates, we still prove the consistency of our Bayesian TBS estimators. Simulation studies and real data analysis demonstrate the advantages of our methods. Another main part of this thesis deals the above challenges from a frequentist standpoint. This model incorporates a penalized likelihood to accommodate skewed response, arising from an epsilon-skew-normal (ESN) distribution. With suitable optimization techniques to handle this two-piece penalized likelihood, our method demonstrates substantial gains in sensitivity and specificity even under high-dimensional settings. We conclude this thesis with a novel Bayesian semi-parametric modal regression method along with its implementation and simulation studies. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2017. / June 9, 2017. / Includes bibliographical references. / Debajyoti Sinha, Professor Directing Dissertation; Miles Taylor, University Representative; Debdeep Pati, Committee Member; Yiyuan She, Committee Member; Yun Yang, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_552145 |
| Contributors | Wang, Libo (authoraut), Sinha, Debajyoti (professor directing dissertation), Taylor, Miles G., 1976- (university representative), Pati, Debdeep (committee member), She, Yiyuan (committee member), Yang, Yun (Professor of Statistics) (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (70 pages), computer, application/pdf |
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