James-Stein型置信椭球及其覆盖概率

JAMES-STEIN TYPE CONFIDENCE ELLIPSOID AND ITS COVERAGE PROBABILITY

本文构造了协方差阵具有非球型结构（未知）的多元正态分布均值的Ｊａｍｅｓ－Ｓｔｅｉｎ 型置信椭球，它能渐近一致改进通常置信椭球的覆盖概率，并给出了改进余项的一致阶， 同时本质改进了文献中有关余项的一致阶。

This paper constructs the Jame-Stein type confidence ellipsoid for the mean of multivariate normal distribution with a class of unknown non-spherical covariance matrix structure. The coverage probability of the usuall confidence ellipsoid is shown to be im proved asmptotically by centering at a Jame-Stein type estimator, and uniform order of the remainder term in the coverage probability expansion is also given.