Optimal Shrinkage Estimation for Heteroscedastic Data

Harvard University, Cambridge MA

Investigators

Abstract

Shrinkage estimators are powerful statistical methods that have profound impact in scientific and engineering applications. They provide efficient tools to pool information from related populations for simultaneous inference -- the data on each population alone often do not lead to the most effective estimation, but by pooling information from the related populations together one can often obtain more accurate estimates for each individual population. Examples of the applications of shrinkage estimators include the analysis of healthcare systems (quality of hospital services, etc.), the analysis of education programs (the effectiveness of teaching programs), the assessment of medical treatments (pooling information from multiple studies or clinical trials), the ranking of multiple genes on their association with diseases, and the comparison of multiple manufacturing processes. This research project will investigate shrinkage estimations in the context of heterogeneous data, aiming to identify optimal ways to conduct shrinkage estimation in various settings. This research project studies and identifies risk-optimal shrinkage estimators under parametric as well as semi-parametric settings for heteroscedastic data. In addition to thorough theoretical investigation, the project includes comprehensive numerical studies and real applications. The research topics include the investigation of optimal shrinkage estimators for heteroscedastic data from non-Gaussian exponential families; the investigation of optimal shrinkage estimators for heteroscedastic data from location-scale families; and the investigation of optimal shrinkage estimators for heteroscedastic data from linear regression models. The research aims to advance the theoretical understanding of shrinkage estimators and also provide powerful techniques for the analysis of data in medical, natural and social sciences, and engineering.