Date Available
8-1-2026
Year of Publication
2024
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Advisor
Dr. Solomon W. Harrar
Abstract
In this dissertation, we investigate three distinct but interrelated problems in analyzing repeated measure data with missing values.
The first project is on semiparametric methods for analyzing repeated measures designs with missing values. A closed-form estimator for the parameters and their asymptotic covariance are derived using block partitioning based on the missing data pattern. We also derive the asymptotic distribution of the estimators and construct test statistics to test hypothesis formulated as linear contrasts of the mean vector.
In the second project, we focus on purely nonparametric methods. In this setup, nonparametric treatment effects are defined as functionals of the distribution functions known as relative effects. The hypothesis is formulated in terms of these functionals. The marginal distribution functions corresponding to the different groups are allowed to be different under the null hypothesis, a phenomenon commonly known as the nonparametric Behrens-Fisher problem. The asymptotic joint distribution of the estimators of treatment effects is derived, along with a consistent estimator of the asymptotic covariance matrix. The method can be applied to both metric and ordered categorical data. Size and power simulation studies of the ANOVA and Wald type tests show satisfactory performance. A dataset on asthma randomized trial is used to illustrate the application of the methods.
For the third project, we address the analysis of multivariate repeated measures data, initially assuming the same missing pattern across all variables. Asymptotically unbiased and consistent estimators of relative effects are developed. Robust tests are proposed based on these estimators and asymptotic distribution. Numerical investigation show favorable performance of our proposed method. Dataset from a metagenomics study in a cohort of human and livestock samples in East Africa is used to illustrate the application of the methods.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2024.368
Recommended Citation
Maity, Swetalina, "Estimation and Testing of Nonparametric Effects of Incomplete Multivariate and Repeated Measures Data" (2024). Theses and Dissertations--Statistics. 80.
https://uknowledge.uky.edu/statistics_etds/80
