SECOND ORDER ASYMPTOTIC VARIANCE OF THE BAYES ESTIMATOR OF A TRUNCATION PARAMETER FOR A ONE-SIDED TRUNCATED EXPONENTIAL FAMILY OF DISTRIBUTIONS

摘要

For a one-sided truncated exponential family of distributions with a truncation parameter γ and a natural parameter θ as a nuisance parameter, the stochastic expansions of the Bayes estimator (γ)Bθ when θ is known and the Bayes estimator (γ)B,(θ)ML plugging the maximum likelihood estimator (MLE) θML in θ of (γ)B,θ when θ is unknown are derived. The second order asymptotic loss of (γ)B,(θ)ML relative to (γ)B,θ is also obtained through their asymptotic variances. Further, it is shown that (γ)B,θ and (γ)B,(θ)ML are second order asymptotically equivalent to the bias-adjusted MLEs (γ)ML*, θ and (γ)ML* when 9 is known and when 9 is unknown, respectively. Some examples are also given.