This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 25
Type: Topic Contributed
Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #306858
Title: A Numerical Comparison of Some Rate-Efficient Nonparametric Estimates
Author(s): Boris Levit*+
Companies: Queen's University
Address: Queen's University, Kingston, ON, K7L3N6, Canada
Keywords: Minimax estimation ; nonparametric regression ; white Gaussian noise ; linear estimators ; low-pass filters ; non-asymptotic approach
Abstract:

Various lower bounds in the minimax estimation of normal means are reviewed. A global lower bound for the minimax risk is proposed and shown to be highly efficient in a non-asymptotic setting.

This bound will be used in the continuous white Gaussian noise nonparametric regression. Some general ellipsoidal and cuboidal functional classes will be introduced in terms of Fourier transforms. These will include classes of entire functions of exponential type, Paley-Wiener classes, Sobolev classes, and other. The efficiency of both minimax linear estimators and minimax low-pass filters will be numerically evaluated, in a non-asymptotic setting.

This outlook helps to understand better the limitations of the purely asymptotic approach. An offhand asymptotic approach to optimal estimation can be seen as very unreliable and, at times, misleading, in the case of moderate sample sizes.


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