Mathematical Sciences: Statistical Models and Methods for Incomplete and Biased Data

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This research focuses on the development of models and methods for statistical analysis of biased, or incomplete, data. Problems will be tackled in three different general research areas: (1) Estimation in Renewal Processes, (2) Semiparametric Models in Selection Bias, and (3) Statistical Models for Cross Sectional Sampling. This work in statistics aims at improving the tools available for handling sampling bias and incompleteness in data acquisition. The recent spread of the AIDS epidemic, and the behavioral issues involved in sampling, diagnosing, and identifying patients present a pressing need for the development of such methods for a variety of complicated biased-sampling schemes. In developing the statistical models and methods, these issues will be addressed.