Statistics Papers

Document Type

Journal Article

Date of this Version

1991

Publication Source

Annals of Statistics

Volume

19

Issue

1

Start Page

329

Last Page

337

DOI

10.1214/aos/1176347985

Abstract

This paper compares three methods for producing lower bounds on the minimax risk under quadratic loss. The first uses the bounds from Brown and Gajek. The second method also uses the information inequality and results in bounds which are always at least as good as those from the first method. The third method is the hardest-linear-family method described by Donoho and Liu. These methods are applied in four examples, the last of which relates to a frequently considered problem in nonparametric regression.

Keywords

information inequality (Cramer-Rao inequality), minimax risk, density estimation, nonparametric regression, estimating a bounded normal mean

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Date Posted: 27 November 2017

This document has been peer reviewed.