Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions

摘要

Bayes sequential estimation in a family of transformed Chi-square distributions using a linex loss function and a cost c 0 for each observation is considered in this paper. It is shown that an asymptotic pointwise optimal rule (A.P.O.) is asymptotically non-deficient, i.e., the difference between the Bayes risk of the A.P.O. rule and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of single observation, as c → 0.