Date of this Version
Journal of Statistical Planning and Inference
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.
© 2006. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.
Bayes risk, harmonic, heat equation, inadmissibility, matching polynomial, Stein's identity, unbiased
Brown, L. D., DasGupta, A., Haff, L. R., & Strawderman, W. E. (2006). The Heat Equation and Stein's Identity: Connections, Applications. Journal of Statistical Planning and Inference, 136 (7), 2254-2278. http://dx.doi.org/10.1016/j.jspi.2005.12.001
Date Posted: 27 November 2017
This document has been peer reviewed.