DEPARTMENT OF STATISTICS
Statistics Colloquium
University of Connecticut
Storrs, Connecticut
The Department of Statistics Cordially invites you to a Colloquium
Zhiqiang Tan
Associate Professor
Department of Statistics
Rutgers University
Improved Minimax Estimation under Heteroscedasticity
ABSTRACT
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. There remain challenging issues on how much the observations with different variances should be shrunk relatively to each other. We propose a new minimax estimator, by approximately minimizing the Bayes risk with a normal prior among a class of minimax estimators where the shrinkage direction is open to specification and the shrinkage magnitude is determined to achieve minimaxity. The proposed estimator has an interesting simple form and is scale adaptive: it can achieve close to the minimum Bayes risk simultaneously over a scale class of normal priors (including the specified prior) and achieve close to the minimax linear risk over a corresponding scale class of hyper-rectangles. For various scenarios in our numerical study, the proposed estimators with extreme priors yield more substantial risk reduction than existing minimax estimators.
DATE: Wednesday, December 4, 2013
TIME: 4:00 p.m.
PLACE: Philip E. Austin Building – Room 105
For more information, contact: Tracy Burke at tracy.burke@uconn.edu