Open Access
VOL. 8 | 2012 A weak functional framework for applications in statistics
Adel Blouza, Dominique Fourdrinier, Patrice Lepelletier

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 90-103 (2012) DOI: 10.1214/11-IMSCOLL807


For the problem of estimating a general loss of the form c(xθ2), Stein’s identity is particularly relevant in deriving unbiased estimators of loss when x is used as an estimate of θ and is distributed as $\mathcal{N}_{p}(\theta,I)$, and when c is the identity function. In [3], Fourdrinier and Lepelletier show that extensions to other distributions (actually, to spherically symmetric distributions) and to general functions c are conceivable, but through another approach involving a Green’s formula. Somewhat surprisingly, the statistical context induces an unusual weak functional framework. The main goal of this paper is to present such an analytic context.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1326.62015
MathSciNet: MR3202505

Digital Object Identifier: 10.1214/11-IMSCOLL807

Primary: 26B20 , 46F10 , 62C05 , 62C12

Keywords: Green formula , loss estimation , Sobolev Spaces , spherically symmetric distributions

Rights: Copyright © 2012, Institute of Mathematical Statistics

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