Degree Type

Dissertation

Date of Award

2011

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Yongzhao Shao

Second Advisor

Jaekwang Kim

Abstract

In statistical analysis, distribution assumptions are often subject to be tested. In this dissertation, the problem of testing two important distribution assumptions, the normal distribution and uniform distribution, is considered. Specifically, a new characterization of multivariate normality based on univariate projections is developed. On the other hand, a powerful affine invariant test of multivariate normality is proposed. Moreover, this dissertation also presents an asymptotic distribution free test of multivariate uniformity based on $m$-nearest neighbors. Both tests have demonstrated good power performance by numerical studies.

Incomplete data is another commonly encountered issue in practice. This dissertation also reports an efficient estimation method for population mean in longitudinal surveys under monotone missing pattern. The proposed method is developed using the generalized method of moments technique by incorporating all the available information at each time point. Efficiency of the method over the direct propensity score type estimator is also demonstrated by limited numerical studies.

DOI

https://doi.org/10.31274/etd-180810-2135

Copyright Owner

Ming Zhou

Language

en

Date Available

2012-04-30

File Format

application/pdf

File Size

112 pages

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