Sliced Inverse Regression is a method for reducing the dimension of the explanatory variables x in non-parametric regression problems. Li (1991) discussed a version of this method which begins with a partition of the range of y into slices so that the conditional covariance matrix of x given y...

To overcome the curse of dimensionality, dimension reduction is important andnecessary for understanding the underlying phenomena in a variety of fields.Dimension reduction is the transformation of high-dimensional data into ameaningful representation in the low-dimensional space. It can be...

Positive and negative predictive values are important measures of accuracy whenone compares the accuracy of diagnostic tests. When more than one diagnostic tests areavailable, one may has to choose one of the possible diagnostic tests due to cost, time, orethical reason. We consider a pair study...

In the first part of the dissertation, we derive two methods for responders analysis in longitudinal data with random missing data. Often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific point in time according to a prespecified threshold...

Considerable recent interest has focused on doubly robust estimatorsfor a population mean response in the presence of incomplete data,which involve models for both the propensity score and the regressionof outcome on covariates. The ``usual" doubly robust estimator mayyield severely biased...

In this thesis, we address issues of model estimation for longitudinal categorical data and of model selection for these data with missing covariates. Longitudinal survey data capture the responses of each subject repeatedly through time, allowing for the separation of variation in the measured...

When sampling from a finite population to estimate the means or totals of K population characteristics of interest, survey designs typically impose the constraint that information on all K characteristics (or data items) is collected from all units in the sample. Relaxing this constraint means...

An important challenge in statistical modeling involves determining an appropriate structural form for a model to be used in making inferences and predictions. Missing data is a very common occurrence in most research settings and can easily complicate the model selection problem. Many useful...

This dissertation is a collection of three stand-alone research papers. Thereby, the class of local polynomial matching estimators is the central object of investigation. The first essay concentrates on applying local polynomial matching methods in order to account for missing data when...