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Robust generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with unknown scale

Dominique Fourdrinier and William E. Strawderman

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Abstract

We consider estimation of the mean vector, θ, of a spherically symmetric distribution with unknown scale parameter σ under scaled quadratic loss. We show minimaxity of generalized Bayes estimators corresponding to priors of the form π(‖θ‖2)ηb where η = 1 / σ2, for π(⋅) superharmonic with a non decreasing Laplacian under conditions on b and weak moment conditions. Furthermore, these generalized Bayes estimators are independent of the underlying density and thus have the strong robustness property of being simultaneously generalized Bayes and minimax for the entire class of spherically symmetric distributions.

Chapter information

Source
James O. Berger, T. Tony Cai and Iain M. Johnstone, eds., Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 249-262

Dates
First available in Project Euclid: 26 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1288099024

Digital Object Identifier
doi:10.1214/10-IMSCOLL617

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures

Keywords
Bayes estimators minimax estimators spherically symmetric distributions location parameter scale parameter quadratic loss superharmonic priors

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Fourdrinier, Dominique; Strawderman, William E. Robust generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with unknown scale. Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown, 249--262, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL617. https://projecteuclid.org/euclid.imsc/1288099024


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References

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