| James—Stein型置信椭球及其覆盖概率 |
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| 引用本文： | 崔恒建. James—Stein型置信椭球及其覆盖概率[J]. 应用数学学报, 2001, 24(3): 404-409 |
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| 作者姓名： | 崔恒建 |
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| 作者单位： | 北京师范大学数学系,北京100875 |
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| 基金项目： | 国家自然科学基金(19971011号)和国家教育部优秀年轻教师基金资助项目. |
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| 摘 要： | 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。
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| 关 键 词： | James－Stein型估计 置信椭球 覆盖概率 协方差阵 多元正态分布 正态随机变量 |
JAMES-STEIN TYPE CONFIDENCE ELLIPSOID AND ITS COVERAGE PROBABILITY |
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| CUI HENGJIAN. JAMES-STEIN TYPE CONFIDENCE ELLIPSOID AND ITS COVERAGE PROBABILITY[J]. Acta Mathematicae Applicatae Sinica, 2001, 24(3): 404-409 |
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| Authors: | CUI HENGJIAN |
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| Abstract: | 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. |
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| Keywords: | Jame-Stein type estimator confidence ellipsoid coverage probability |
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