On the small N Performance of bootstrap and bayes extended and unextended set compound rules for classification between N( -1,1)and N(1,1)†

We study a situation in which N independent classifications between N(- 1; 1) and N(1,1) are to be faced simultaneously. This problem was the featured example in Robbins′ (1951) introduction of the compound decision problem and has been used many times since to illustrate various aspects of the developing theory of compound and empirical Bayes decisions. We here study the moderate N risk behavior of recently developed so-called “extended” bootstrap and Bayes procedures for the prob!em. The behavicr of :hese rules is compared to that of the bootstrap and Bayes rules originally suggested by Robbins.