论文信息 - EMPIRICAL BAYES AND COMPOUND ESTIMATION OF NORMAL MEANS

EMPIRICAL BAYES AND COMPOUND ESTIMATION OF NORMAL MEANS

Dedicated to Herbert Robbins on his 80th birthday Abstract: This article concerns the canonical empirical Bayes problem of estimating normal means under squared-error loss. General empirical estimators are derived which are asymptotically minimax and optimal. Uniform convergence and the speed of convergence are considered. The general empirical Bayes estimators are compared with the shrinkage estimators of Stein (1956) and James and Stein (1961). Estimation of the mixture density and its derivatives are also discussed.

Cun-Hui Zhang | Cun-Hui Zhang

[1] C. Stein,et al. Estimation with Quadratic Loss , 1992 .

[2] H. Robbins. Some Thoughts on Empirical Bayes Estimation , 1983 .

[3] B. Lindsay. Using Empirical Partially Bayes Inference for Increased Efficiency , 1985 .

[4] P. Hall,et al. Optimal Rates of Convergence for Deconvolving a Density , 1988 .

[5] H. Robbins. Asymptotically Subminimax Solutions of Compound Statistical Decision Problems , 1985 .

[6] Cun-Hui Zhang. Fourier Methods for Estimating Mixing Densities and Distributions , 1990 .

[7] Jianqing Fan. On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems , 1991 .

[8] H. Robbins. An Empirical Bayes Approach to Statistics , 1956 .

[9] R. Carroll,et al. Deconvolving kernel density estimators , 1987 .

[10] E. George. Minimax Multiple Shrinkage Estimation , 1986 .

[11] David Edelman,et al. Estimation of the Mixing Distribution for a Normal Mean with Applications to the Compound Decision Problem , 1988 .

[12] Michel Loève,et al. Probability Theory I , 1977 .