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二阶无偏贝叶斯估计量的先验构造AI 解读

Summary Asymptotically unbiased priors, introduced by Hartigan (1965), are designed to achieve second-order unbiasedness of Bayes estimators. This paper extends Hartigan’s framework to non-independent-and-identically-distributed models by deriving a system of partial differential equations that characterizes asymptotically unbiased priors. Furthermore, we establish a necessary and sufficient condition for the existence of such priors and propose a simple procedure for…

改进等变估计量的统一方法AI 解读

In the point and interval estimation of the variance of a normal distribution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth procedures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of normal, lognormal,…

Pitman 接近性准则意义下的 Stein 悖论AI 解读

The dominance and related optimality properties of the usual Stein-rule or shrinkage estimators are typically developed for quadratic error loss functions. It is shown that under the classical Pitman closeness criterion the Stein-rule estimators possess a similar dominance property when the "closeness" measure is based on suitable quadratic norms.

两个正态总体共同均值的可容许极小极大估计AI 解读

Consider the problem of estimating the common mean $\mu$ of two normal populations with unknown variances $\sigma^2_1$ and $\sigma^2_2$ under the quadratic loss $(\hat{\mu} - \mu)^2/\sigma^2_1$. A family of minimax estimators with smaller risk than the sample mean in the first population is given, out of which admissible minimax estimators are developed. A class of better estimators of $\mu$ under squared-error loss, which is wider than found by Bhattacharya, is obtained.