Abstract
We study estimation of the parameter p of a r.v. x ∼ Bin(p,n) using the prior hypothesis that p equals a prepecified value Po when we entertain the possibility that Po is not the right value of p, which then could be any value in (0.1). We apply notions of Hodges and Lehmann (1952), Bickel (1984) and Berger (1982) to obtain (biased) estimators which do well under the hypothesis that p = po at a small price in maximum risk. A number of examples and comparisons are discussed at the end of the paper.