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June, 1983 Robustness of Ferguson's Bayes Estimator of a Distribution Function
Robert Hannum, Myles Hollander
Ann. Statist. 11(2): 632-639 (June, 1983). DOI: 10.1214/aos/1176346168


We derive an explicit expression for the Bayes risk (using weighted squared error loss) of Dalal's Bayes estimator of a symmetric distribution under a $\mathscr{G}$-invariant Dirichlet process prior. We compare this risk to the risk of Ferguson's estimator of an arbitrary distribution under the $\mathscr{G}$-invariant prior. This enables us to (i) assess the savings in risk attained by incorporating known symmetry structure in the model and (ii) provide information about the robustness of Ferguson's estimator against a prior for which it is not Bayes.


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Robert Hannum. Myles Hollander. "Robustness of Ferguson's Bayes Estimator of a Distribution Function." Ann. Statist. 11 (2) 632 - 639, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0532.62018
MathSciNet: MR696074
Digital Object Identifier: 10.1214/aos/1176346168

Primary: 62G05
Secondary: 62G35

Keywords: $\mathscr{G}$-invariant Dirichlet process , Bayes estimator , symmetric distribution

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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