## Institute of Mathematical Statistics Collections

### A weak functional framework for applications in statistics

#### Abstract

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.

#### Chapter information

Source
Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 90-103

Dates
First available in Project Euclid: 14 March 2012

https://projecteuclid.org/euclid.imsc/1331731614

Digital Object Identifier
doi:10.1214/11-IMSCOLL807

Mathematical Reviews number (MathSciNet)
MR3202505

Zentralblatt MATH identifier
1326.62015

Rights

#### Citation

Blouza, Adel; Fourdrinier, Dominique; Lepelletier, Patrice. A weak functional framework for applications in statistics. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 90--103, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL807. https://projecteuclid.org/euclid.imsc/1331731614