AN INFORMATION INEQUALITY FOR THE BAYES RISK IN A FAMILY OF UNIFORM DISTRIBUTION

Abstract

For a family of uniform distribution on the interval [θ − (1/2) , θ − (1/2)], the informationinequality for the bayes risk of any estimator of θ is given under the quadratic loss and the uniform priordistribution on an interval [−c, c]. The lower bound for the Bayes risk is shown to be sharp. And also thelower bound for the limit inferior of Bayes risk as c → ∞ is seen to be attained by the mid-range estimator