A Bayes minimax result for spherically symmetric unimodal distributions

作者：Fourdrinier Dominique^*; Mezoued Fatiha; Strawderman William E

来源：Annals of the Institute of Statistical Mathematics, 2017, 69(3): 543-570.

DOI：10.1007/s10463-016-0553-1

• Bayes estimators
• minimax estimators
• Spherically symmetric distributions
• Location parameter
• Unimodal densities
• Quadratic loss
• Superharmonic priors

We consider Bayesian estimation of the location parameter of a random vector X having a unimodal spherically symmetric density for a spherically symmetric prior density . In particular, we consider minimaxity of the Bayes estimator under quadratic loss. When the distribution belongs to the Berger class, we show that minimaxity of is linked to the superharmonicity of a power of a marginal associated to a primitive of f. This leads to proper Bayes minimax estimators for certain densities F (parallel to x - theta parallel to(2)).

• 出版日期2017-6