Date of Award
Doctor of Philosophy
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.
Zhou, Ming, "Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data" (2011). Graduate Theses and Dissertations. 11207.