Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

A Note On Unbiased Bayes Estimates

P. J. Bickel and C. L. Mallows
The American Statistician
Vol. 42, No. 2 (May, 1988), pp. 132-134
DOI: 10.2307/2684486
Stable URL: http://www.jstor.org/stable/2684486
Page Count: 3
  • Download ($14.00)
  • Cite this Item
A Note On Unbiased Bayes Estimates
Preview not available

Abstract

Suppose x and y are random variables that satisfy both E(x∣y) = y and E(y∣x) = x. If we think of x as an observation and y as a parameter, then the first relation says that the parameter y is the mean of x and the second says that the Bayes estimate of this parameter (i.e., the posterior mean of the parameter, given the observation) is unbiased. We show that provided either (a) E|x| is finite or (b) x is non-negative, all of the probability must be concentrated on the set {x = y}; but if both (a) and (b) fail then this conclusion does not follow. We give an explicit counterexample. If the joint distribution is allowed to be improper (but with proper conditionals), then (b) does not imply the conclusion; we give both continuous and discrete counterexamples. If the support of either x or y has no point of accumulation, however, the conclusion does follow.

Page Thumbnails

  • Thumbnail: Page 
132
    132
  • Thumbnail: Page 
133
    133
  • Thumbnail: Page 
134
    134