期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：03
出版社：Indian Statistical Institute
摘要：We consider the problem of estimating the parameter $p$ of a Binomial$(n,p)$ distribution when $p$ lies in the symmetric interval about $1/2$ of the form $[a,1-a]$, with $a \in (0,1/2)$. For a class of loss functions, which includes the important cases of squared error and information-normalized losses, we investigate conditions for which the Bayes estimator, $\delta_{BU}$, with respect to a symmetric prior concentrated on the end points of the parameter space is minimax. Our conditions are of the form $1-2a \leq c(n)$ with $c(n)= O(n^{-1/2})$, and various analytical evaluations, lower and upper bounds, and numerical evaluations are given for $c(n)$. For instance, the simple condition $1-2a \leq {1}/{\sqrt{2n}}$ guarantees, for all $n \geq 1$, the minimaxity of $\delta_{BU}$ under both squared error and information-normalized losses.
