Robustness of Ferguson's Bayes estimator of a distribution function
type: Item
instance of: scholarly article
title: Robustness of Ferguson's Bayes estimator of a distribution function
zbMATH Open document ID: 0532.62018
author: Myles Hollander
author: Robert C. Hannum
published in: The Annals of Statistics
publication date: 1983-01-01T00:00:00Z
review text: An explicit expression for the Bayes risk of \textit{S. R. Dalal's} [Stochastic Processes Appl. 9, 99-107 (1979; Zbl 0415.60035)] Bayes estimator of a symmetric distribution under a \({\mathcal G}\)-invariant Dirichlet process prior is derived and this risk is compared to the risk of \textit{T. S. Ferguson's} [Ann. Stat. 1, 209-230 (1973; Zbl 0255.62037)] estimator of an arbitrary distribution under the \({\mathcal G}\)-invariant prior. This enables the authors to assess the savings in risk attained by incorporating known symmetry structure in the model and to provide information about the robustness of Ferguson's estimator against a prior which is not Bayes.
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 3844821
zbMATH Keywords: robustness of Ferguson estimator
zbMATH Keywords: explicit expression
zbMATH Keywords: Bayes risk
zbMATH Keywords: symmetric distribution
zbMATH Keywords: invariant Dirichlet process
zbMATH Keywords: invariant prior
zbMATH Keywords: symmetry structure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346168
OpenAlex ID: W2074498280
DOI: 10.1214/AOS/1176346168
description: scientific article; zbMATH DE number 3844821