Radial estimates and the test for sphericity
Radial estimates and the test for sphericity
复制标题
径向估计和球形度检验
DOI：
10.1093/biomet/69.2.429
复制
发表时间：
1982
期刊：
影响因子：
2.7
通讯作者：
David E. Tyler
中科院分区：
文献类型：
--
作者：
David E. Tyler
给出了具有径向分布的随机对称矩阵的前两个矩。这一结果使人们能够将基于样本协方差矩阵的渐近过程推广到基于一类正定矩阵参数估计的过程。本类包括椭圆总体散点矩阵的最大似然估计和散点矩阵的仿射不变鲁棒估计。并说明了结果在球度测试中的应用。
SUMMARYThe first two moments for random symmetric matrices with radial distributions are given. This result enables one to generalize asymptotic procedures based on the sample covariance matrix to procedures based on a class of estimates for a positive-definite matrix parameter. This class includes the maximum likelihood estimates for the scatter matrix of an elliptical population, and affine-invariant robust estimates of a scatter matrix. Application of the results to the test for sphericity is illustrated.