Preprint: "Minimax Estimation with Thresholding and its application to Wavelet Analysis" by Harrison H. Zhou and J.T. Gene Hwang

[Harrison H. Zhou (hbzhou@math.cornell.edu)]

The following paper has been revised for the Annals of Statistics.

AUTHORS

Harrison H. Zhou and J.T. Gene Hwang
Cornell University

ABSTRACT

Many statistical practices involve selecting a model (a reduced model from the full model) and then use it to do estimation with possible thresholding. Is it possible to do so and still come up with an estimator always better than the naive estimator without model selection? The James-Stein estimator allows us to do so. However, James-Stein estimator considers only one reduced model, the origin. What should be more desirable is select a data chosen reduced model (of an arbitrary dimension) and then do estimation. In this paper, we constructed such estimators. We apply the estimators to wavelet analysis. The estimators perform the best among the well-known estimators trying to do model selection and estimation at the same time. Some of our estimators are also known to be asymptotically optimal.

The preprint is available at
http://www.math.cornell.edu/~hbzhou/