Publication Date

2021

Document Type

Dissertation

Committee Members

Shuxia Sun, Ph.D. (Committee Co-Chair); Zheng Xu, Ph.D. (Committee Co-Chair); Weizhen Wang, Ph.D. (Committee Member); Yang Liu, Ph.D. (Committee Member); Joseph Houpt, Ph.D. (Committee Member)

Degree Name

Doctor of Philosophy (PhD)

Abstract

This dissertation includes two topics, Bickel-Rosenblatt test based on tilted density estimation for autoregressive models and deep merged survival analysis on cancer study using multiple types of bioinformatic data. In the first topic study, we consider the goodness of fit test the error density of linear and nonlinear autoregressive models using tilted kernel density estimation based on residuals. Bickel-Rosenblatt test statistic is based on the integrated square error of non-parametric error density estimation and a smoothed version of the parametric fit of the density. It is shown that the new type of Bickel-Rosenblatt test statistics behaves asymptotically the same as the one with conventional estimators based on true unobservable errors. We show technique details, simulation studies and real data analysis to present the performance of the new test statistic. The second topic is about deep survival analysis on cancer study. For cancer survival prediction, we propose to use deep merged survival networks with network layers at high levels merged together for better integration of information from multiple heterogeneous data sets to improve prediction accuracy. We conducted simulation studies to compare our proposed method with other methods in the literature under a range of scenarios. We conducted real data analysis based on breast cancer TCGA data to illustrates the advantage of our method over literature methods, and the advantage of using multiple data sets over using only one data set.

Page Count

127

Department or Program

Department of Mathematics and Statistics

Year Degree Awarded

2021

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