An application of G-minimax techniques to the problem of fixed precision estimation of the binomial

Abstract

Estimation of the binomial probability θ is considered for the loss function in which the loss is zero if the estimate θcirc;(x) is within a predetermined distance △,△/2 from θ, and the loss is one if θcirc;(x) is more than △,△/2 from θ. An estimator that is optimal within a specified class G of symmetric beta priors isfound, using criteria of minimax risk and minimax integrated risk. The behavior of this G-minimaxestimator, which turns out to be the Bayes estimator based on the uniform prior, is then compared with that of the maximum likelihood estimator.