Using empirical partially Bayes inference for increased efficiency. (English) Zbl 0601.62044

Lindsay, Bruce G.

Ann. Stat. 13, 914-931 (1985).

The author shows how empirical partially Bayes methods can be utilized as a means for improving the efficiency of an estimator of the structural parameter in a class of problems in which the number of nuisance parameters increases to infinity. It is proposed to estimate the structural parameter in an asymptotically unbiased way and apply James- Stein shrinkage to the nuisance parameter estimators. It is shown that when the shrinkage estimators are carefully chosen, this yields estimators generally more efficient than the maximum likelihood one.

Reviewer: J.Melamed

MSC:

62F12	Asymptotic properties of parametric estimators
62F10	Point estimation
62F15	Bayesian inference

Keywords:

James-Stein effect; score function; James-Stein estimators; consistency; empirical partially Bayes methods; efficiency; structural parameter; nuisance parameters; asymptotically unbiased; James-Stein shrinkage; maximum likelihood