OPTIMAL RANK-BASED TESTING FOR PRINCIPAL COMPONENTS
OPTIMAL RANK-BASED TESTING FOR PRINCIPAL COMPONENTS
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DOI：
10.1214/10-aos810
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发表时间：
2010-12-01
影响因子：
4.5
通讯作者：
Verdebout, Thomas
中科院分区：
文献类型：
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作者：
Hallin, Marc;Paindaveine, Davy;Verdebout, Thomas
本文给出了椭圆族中协方差矩阵或散布矩阵的特征向量和特征值的参数和基于秩的最优检验。参数检验推广了安德森（1963）的高斯似然比检验以及Davis（1977）和泰勒（1981，1983）对它们的伪高斯鲁棒性。基于秩的检验解决了一类更广泛的问题，其中协方差矩阵不需要存在，主成分与更一般的散布矩阵相关联。所提出的测试被证明优于日常实践的有效性的角度来看，从效率的角度来看。这是通过利用Le Cam理论的局部渐近正常的实验，在非标准的情况下，然而，一个弯曲的参数化。我们得出的曲线实验的结果是独立的利益，并可能适用于其他情况下。
This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Davis (1977) and Tyler (1981, 1983). The rank-based tests address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general scatter matrices. The proposed tests are shown to outperform daily practice both from the point of view of validity as from the point of view of efficiency. This is achieved by utilizing the Le Cam theory of locally asymptotically normal experiments, in the nonstandard context, however, of a curved parametrization. The results we derive for curved experiments are of independent interest, and likely to apply in other contexts.