Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed
Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed
复制标题
总体特征值无限分散时Wishart矩阵的特征值和特征向量的分布
DOI：
10.1016/j.jmva.2004.05.003
复制
发表时间：
2005
影响因子：
0.8
通讯作者：
A. Takemura
中科院分区：
文献类型：
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作者：
A. Takemura
当总体特征值变得无限离散时，我们考虑Wishart矩阵的特征值和特征向量的渐近联合分布。我们证明了归一化样本特征值和样本特征向量的相关元素都是渐近相互独立分布的。归一化样本特征值的极限分布是具有不同自由度的卡方分布，特征向量的相关元素的分布是标准正态分布。作为这一结果的一个应用，我们研究了关于Stein损失函数和二次损失函数的Wishart分布总体协方差矩阵估计的尾极小问题。在温和的正则性条件下，我们证明了当样本特征值变得无限离散时，一类广义的尾极小极大估计的行为是相同的。
We consider the asymptotic joint distribution of the eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues become infinitely dispersed. We show that the normalized sample eigenvalues and the relevant elements of the sample eigenvectors are asymptotically all mutually independently distributed. The limiting distributions of the normalized sample eigenvalues are chi-squared distributions with varying degrees of freedom and the distribution of the relevant elements of the eigenvectors is the standard normal distribution. As an application of this result, we investigate tail minimaxity in the estimation of the population covariance matrix of Wishart distribution with respect to Stein's loss function and the quadratic loss function. Under mild regularity conditions, we show that the behavior of a broad class of tail minimax estimators is identical when the sample eigenvalues become infinitely dispersed.
DOI：
--
发表时间：
2001
期刊：
The Annals of Statistics Vol.29, No.2
影响因子：
--
作者：
Satoshi Kuriki;Akimichi Takemura
通讯作者：
Akimichi Takemura