Robustness of Ferguson's Bayes estimator of a distribution function
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.
scientific article; zbMATH DE number 3844821