On using the kernel method for functional estimation with current status data

Abstract

To implement Yang's (1999) kernel estimator method, an important issue is the choice of bandwidth. It is well-known that the performance of kernel estimators depend upon the bandwidth. Furthermore, Yang's (1999) method uses the ratio of two kernel estimators which may be more sensitive to the choice of bandwidth. Our goal is to investigate the choice of bandwidth and evaluate the performance of the corresponding kernel estimators. The NPMLE will also be included in the studies for comparison. By comparing the mean square error of the kernel estimator against the NPMLE of Groeneboom and Wellner (1992), the kernel estimator was found to behave quite well under the given testing conditions.

This thesis is organized as follows: The NPMLE method for functional estimation is introduced in Chapter II. Yang's kernel estimator method is introduced in Chapter III. In Chapter IV, we explain the procedures for evaluating the best choice of bandwidth. We analyze and display the results from the computer simulations in Chapter V. Finally, conclusions are drawn in Chapter VI.