|
Abstract:
|
This dissertation addresses the problem of model specification testing in situa-
tions where data are incomplete, utilizing the existing theory of non-degenerate and weakly
degenerate U- and V-statistics. The first two chapters lay the theoretical groundwork by pre-
senting essential concepts related to U- and V-statistics and the general mathematical frame-
work of missing data analysis, which serve as the foundation for the new results developed in
subsequent chapters.
In Chapter 3, a novel test for assessing the missing completely at random (MCAR) assump-
tion is introduced. This test demonstrates improved control of the type I error rate and supe-
rior power performance compared to the main competitor across the majority of the simulated
scenarios examined.
Chapter 4 explores the application of Kendall’s test for independence in the presence of
MCAR data. It provides both theoretical insights and simulation-based comparisons of the
complete-case analysis and median imputation, pointing out their individual advantages and
drawbacks.
Chapter 5 focuses on testing for multivariate normality when data are incomplete. It rig-
orously establishes the validity of the complete-case approach under MCAR and proposes a
bootstrap method to approximate p -values when imputation is employed. Additionally, vari-
ous imputation techniques are evaluated with respect to their impact on the type I error and
the power of the test.
Finally, Chapter 6 adapts the energy-based two-sample test to handle missing data by intro-
ducing a weighted framework that makes full use of all available observations. Alongside some
theoretical developments, the chapter presents two distinct bootstrap algorithms for p -value
estimation under this approach. Additionally, the performance of several imputation methods
is examined in this context, and appropriate bootstrap algorithm is proposed for that setting. |