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

Year 2002, Volume: 5 Issue: 1, 1 - 6, 01.01.2002

Nao Ohyauchi Masafumi Akahira.

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

Keywords

Cram´er-Rao inequality , Bayes Estimator , lower bound , mid-range

References

• Akahira M. and Takeuchi K., (1995), Non-Regular Statistical Estimator. Lecture Notes in Statistics 107, Springer, New York.
• Akahira M. and Takeuchi K., (2001), Information inequalities in a family of uniform distributions, Ann. Inst. Statist. Math., 53, 427-435.
• Khatri, C.G., (1980), Unified treatment of Cram´er-Rao bound for the non-regular density functions, J.Statist. Plann. Inference 4, 75-79.
• M´ori T.F., (1983), Note on the Cram´er-Rao in the nonregular case: The family of uniform distribution, J.Statist. Plann. Inference 7, 353-358.
• Vincze I., (1979), Note on the Cram´er-Rao in the nonregular case, In: Contributions to Statistics, The J. H´ ajeck Memorial Volume, Prague, 253-262