Statistics Papers

Document Type

Journal Article

Date of this Version

7-1-2006

Publication Source

Journal of Statistical Planning and Inference

Volume

136

Issue

7

Start Page

2254

Last Page

2278

DOI

10.1016/j.jspi.2005.12.001

Abstract

This article presents two expectation identities and a series of applications. One of the identities uses the heat equation, and we show that in some families of distributions the identity characterizes the normal distribution. We also show that it is essentially equivalent to Stein's identity. The applications we have presented are of a broad range. They include exact formulas and bounds for moments, an improvement and a reversal of Jensen's inequality, linking unbiased estimation to elliptic partial differential equations, applications to decision theory and Bayesian statistics, and an application to counting matchings in graph theory. Some examples are also given.

Copyright/Permission Statement

© 2006. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

Bayes risk, harmonic, heat equation, inadmissibility, matching polynomial, Stein's identity, unbiased

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Date Posted: 27 November 2017

This document has been peer reviewed.