Author ORCID Identifier
https://orcid.org/0009-0006-9311-2985
Date Available
7-25-2026
Year of Publication
2024
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Statistics
First Advisor
Dr. Solomon W. Harrar
Abstract
In this dissertation, we study projection-based methods to testing problems for high-dimensional data. We also investigate inferential methods for matrix variate data with block compound symmetry (BCS) covariance structure. The research reported in dissertation consists of three projects.
The first project addresses power loss and ill-conditioned error covariance estimates commonly faced by multivariate tests in high-dimensional settings. To overcome these challenges, previous approaches avoided correlations in constructing test statistics, but this required strong assumptions about covariance matrices and dependence structures. More recently, some methods have incorporated correlations by employing random projection into a lower-dimensional space. We develop a unified framework for exact inference using random projections. We propose suitable test statistics and investigate the null distribution. We conduct simulation studies to evaluate the power performance and robustness of our method under nonnormality and other variations of model parameters. Finally, we illustrate the practical utility of our approach by analyzing transcriptome data from an asthma study.
In the second project, we propose projection-based solutions to test equality of mean vectors and equality of mean subvectors under general conditions. For the former, bootstrap tests are proposed, whereas for the latter, an approximate test is examined. Comparative studies were conducted to evaluate the performances of the proposed methods when the data are not necessarily normal or when heteroscedasticity exists.
Meanwhile, in the third project, the goal is to test the equality of mean submatrices for matrix variate data. Here, we restrict our study to low-dimension. Under BCS covariance structure, we propose a Lawley-Hotelling’s type test statistic and derive its null distribution. We also propose an approximation to the null distribution using convolution of Generalized-F distributions. We evaluate the numerical performance of the tests and the approximate null distribution with a simulation study. Finally, we apply the test to multivariate repeated-measures data on cerebral metabolism in epileptic patients.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2024.366
Recommended Citation
Mitra, Shouryya, "High-Dimensional Tests and Projection Methods: Subvector Analysis and Matrix Variate Data" (2024). Theses and Dissertations--Statistics. 78.
https://uknowledge.uky.edu/statistics_etds/78
