Analysis of Absolute Deviation, Inference and Model Selection

Columbia University, New York NY

Investigators

Abstract

This project develops a comprehensive approach to estimation, model selection and inferences for certain regression models, with applications to health sciences, economics, astronomy as well as other disciplines of scientific investigations. Various parts of the project are connected through several key components: computational aspect is handled by linear programming, inferences by simulation-based resampling, simultaneous estimation and model selection by suitably constructed penalty functions, and asymptotic properties by empirical process theory. The investigator develops efficient algorithms for parameter estimation and distributional approximation, establishes small and large sample properties, and extends the methods and theory to data with censoring, truncation or other kind of non-random missingness. This research project is motivated by and closely related to many important areas of scientific disciplines, including health and life sciences, economics, astronomy and sociology. It develops new tools to assess health risks, drugs and treatments effects and genetic variations, to analyze policy formation, such as intervention in unemployment and health insurance, as well as to understand astronomical phenomena. It provides a platform to attract and train students with tools for multi-disciplinary applications.