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

For a family of uniform distribution on the interval [8 - (1/2), e - (1/2)]\u27 the informationinequality for the bayes risk of any estimator of e is given under the quadratic Joss 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 -jo 00 is seen to be attained by the mid-range estimator