Choice of hierarchical priors: Admissibility in estimation of normal means

DOI10.1214/aos/1032526950zbMath0865.62004OpenAlexW2077020715WikidataQ56286879 ScholiaQ56286879MaRDI QIDQ1816965

William E. Strawderman, James O. Berger

Publication date: 1 December 1996

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1032526950

zbMATH Keywords

shrinkage estimationinadmissibilitymean-squared errorJeffreys priorimproper priorsshrinkage priorhyperparametershierarchical Bayesian modeling of normal meanshierarchical priors for normal meanshypermeanshypervarianceproper posteriors

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Bayesian inference (62F15) Admissibility in statistical decision theory (62C15)

Related Items

A class of admissible estimators of multiple regression coefficient with an unknown variance, Optimal shrinkage estimation of mean parameters in family of distributions with quadratic variance, Empirical estimates for heteroscedastic hierarchical dynamic normal models, On minimaxity and admissibility of hierarchical Bayes estimators, A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function, Prior distributions for objective Bayesian analysis, The matrix-F prior for estimating and testing covariance matrices, Stein estimation for spherically symmetric distributions: recent developments, Posterior propriety and admissibiity of hyperpriors in normal hierarchical models, An objective prior for hyperparameters in normal hierarchical models, Estimating the mean and variance of a high-dimensional normal distribution using a mixture prior, Evaluating default priors with a generalization of Eaton's Markov chain, Neuronized Priors for Bayesian Sparse Linear Regression, Larry Brown's contributions to parametric inference, decision theory and foundations: a survey, Larry Brown's work on admissibility, Dominance properties of constrained Bayes and empirical Bayes estimators, Hierarchical Bayes, maximum a posteriori estimators, and minimax concave penalized likelihood estimation, On SURE estimates in hierarchical models assuming heteroscedasticity for both levels of a two-level normal hierarchical model, Integrated likelihood methods for eliminating nuisance parameters. (With comments and a rejoinder)., SURE Estimates for a Heteroscedastic Hierarchical Model, Posterior property in nonparametric mixed effects model, Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance, Admissibility and minimaxity of Bayes estimators for a normal mean matrix, The interplay of Bayesian and frequentist analysis, Proper Bayes minimax estimators of the normal mean matrix with common unknown variances, Noninformative priors and frequentist risks of Bayesian estimators of vector-autoregressive models, Minimum message length shrinkage estimation, Dynamic hierarchical models: an extension to matrix-variate observations.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Statistical decision theory and Bayesian analysis. 2nd ed
• A robust generalized Bayes estimator and confidence region for a multivariate normal mean
• Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss
• Proper Bayes minimax estimators of the multivariate normal mean vector for the case of common unknown variances
• Subjective hierarchical Bayes estimation of a multivariate normal mean: On the frequentist interface
• Information Measures and Bayesian Hierarchical Models
• A Bayesian Approach to Ranking and Selection of Related Means With Alternatives to Analysis-of-Variance Methodology
• Parametric Empirical Bayes Inference: Theory and Applications
• Proper Bayes Minimax Estimators of the Multivariate Normal Mean
• Admissible Estimators, Recurrent Diffusions, and Insoluble Boundary Value Problems