Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Xiangrong Yin
Dr. Richard Kryscio
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)
Wang, Pei, "DIMENSION REDUCTION TECHNIQUES IN REGRESSION" (2021). Theses and Dissertations--Statistics. 57.
Available for download on Friday, July 21, 2023