Title: Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss

Author(s): Malay Ghosh and Tatsuya Kubokawa
Issue: Volume 81 Series A Part 1 Year 2019
Pages: 70 -- 83
We consider the problem of simultaneous estimation of two population means when one suspects that the two means are nearly equal. It is shown that the hierarchical empirical Bayes estimators which shrink the sample means towards the suspected hypothesis dominate the sample mean vectors in simultaneous estimation under the divergence loss function.
Primary 62C20; Secondary 62C12
Keywords and phrases: Dominance property, Hellinger divergence, Kullback- Leibler divergence, Minimaxity, Risk function, Shrinkage estimator, Simultaneous estimation, Stein phenomenon