Statistics Papers

Document Type

Journal Article

Date of this Version

3-2008

Publication Source

Journal of Multivariate Analysis

Volume

99

Issue

3

Start Page

421

Last Page

436

DOI

10.1016/j.jmva.2006.11.010

Abstract

The connections between information pooling and adaptability as well as superefficiency are considered. Separable rules, which figure prominently in wavelet and other orthogonal series methods, are shown to lack adaptability; they are necessarily not rate-adaptive. A sharp lower bound on the cost of adaptation for separable rules is obtained. We show that adaptability is achieved through information pooling. A tight lower bound on the amount of information pooling required for achieving rate-optimal adaptation is given. Furthermore, in a sharp contrast to the separable rules, it is shown that adaptive non-separable estimators can be superefficient at every point in the parameter spaces. The results demonstrate that information pooling is the key to increasing estimation precision as well as achieving adaptability and even superefficiency.

Copyright/Permission Statement

© 2008. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

adaptability, Bayes rules, information pooling, minimax, minimum risk inequalities, nonparametric regression, orthogonal series, separable rules, superefficiency, wavelets, white noise

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Date Posted: 27 November 2017

This document has been peer reviewed.