Date of Award

2018

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Yanyuan Ma

Abstract

The development of science and technology has enabled the use of more covariates. As a result, it has become more difficult to identify dependencies among many covariates. Dimension reduction provides an efficient way to handle this issue by summarizing the effect of covariates via a few linear combinations of covariates. In this dissertation, two methodologies for real-life problems are provided by using dimension reduction equipped with semiparametric theory. The use of semiparametrics allows maximal flexibility of the model by letting some features of the model completely unspecified, while we still enjoy the interpretability of the model through estimating the parameters of interest. The last two chapters in this work present contributions to classification and pathway activity estimation: (1) we propose an optimal semiparametric linear classifier for two groups and show that the estimator outperforms any other linear classifiers; (2) we offer a two-stage analysis for high-dimensional breast cancer survival data through combining a factor model and the general index model for survival data.

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