Date Available

7-21-2023

Year of Publication

2021

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Statistics

First Advisor

Dr. Xiangrong Yin

Second Advisor

Dr. Richard Kryscio

Abstract

Because of the advances of modern technology, the size of the collected data nowadays is larger and the structure is more complex. To deal with such kinds of data, sufficient dimension reduction (SDR) and reduced rank (RR) regression are two powerful tools. This dissertation focuses on these two tools and it is composed of three projects. In the first project, we introduce a new SDR method through a novel approach of feature filter to recover the central mean subspace exhaustively along with a method to determine the dimension, two variable selection methods, and extensions to multivariate response and large p small n scenarios. In the second project, we propose a novel SDR method by minimizing the distance between the population basis and the sample directions and provide a cross-validation method to determine dimension. In large p small n case, by adding a group lasso type penalty term to the objective function, simultaneous dimension reduction and variable selection are achieved. In the third project, we propose a new model by applying the RR idea to multinomial logistic regression (MLR) and combining RR-MLR with the first-order Markov Chain. Then, the model is applied to a dataset from a longitudinal study of aging and dementia.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2021.255

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