Nonparametric covariance estimation in multivariate distributions

被引：0
|
作者：
Detlef Plachky
Andrew L. Rukhin
机构：
[1] University of Münster,
[2] Institute for Mathematical Statistics,undefined
[3] Einsteinstr. 62,undefined
[4] D-48149 Münster,undefined
[5] Germany,undefined
[6] Department of Mathematics & Statistics,undefined
[7] University of Maryland at Baltimore County,undefined
[8] Baltimore,undefined
[9] MD 21250,undefined
[10] USA (e-mail: rukhin@math.umbc.edu),undefined
来源：
Metrika | 1999年 / 50卷
关键词：
Key words: Covariance estimation, Eigenvalues, Kurtosis coefficient, Matrix quadratic loss, Sample covariance matrix, Unbiased estimator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The estimation problem of the unknown covariance matrix of a multivariate distribution with the known mean is studied under a matrix-valued quadratic loss function. The conditions on the sample sizes for the best unbiased estimator to have a smaller risk than the sample covariance matrix is established. The former estimator is completely (without exceptional sets of Lebesgue measure zero) characterized by its expectation in the class of all multivariate distributions with zero mean and finite fourth moments.
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页码：131 / 136
页数：5
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