Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size Export

@article{citeulike:6032066, abstract = {This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting distribution of these tests as dimensionality and sample size go to infinity together, with their ratio converging to a finite nonzero limit. We find that the existing test for sphericity is robust against high dimensionality, but not the test for equality of the covariance matrix to a given matrix. For the latter test, we develop a new correction to the existing test statistic that makes it robust against high dimensionality.}, author = {Ledoit, Olivier and Wolf, Michael}, citeulike-article-id = {6032066}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/1558696}, citeulike-linkout-1 = {http://www.jstor.org/stable/1558696}, doi = {10.2307/1558696}, issn = {00905364}, journal = {The Annals of Statistics}, keywords = {covariance, hypothesis-testing, statistics}, number = {4}, pages = {1081--1102}, posted-at = {2009-10-29 13:00:49}, priority = {0}, publisher = {Institute of Mathematical Statistics}, title = {Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size}, url = {http://dx.doi.org/10.2307/1558696}, volume = {30}, year = {2002} }

TY - JOUR ID - citeulike:6032066 L3 - citeulike-article-id:6032066 N2 - This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting distribution of these tests as dimensionality and sample size go to infinity together, with their ratio converging to a finite nonzero limit. We find that the existing test for sphericity is robust against high dimensionality, but not the test for equality of the covariance matrix to a given matrix. For the latter test, we develop a new correction to the existing test statistic that makes it robust against high dimensionality. IS - 4 JF - The Annals of Statistics SN - 00905364 EP - 1102 TI - Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size PB - Institute of Mathematical Statistics VL - 30 SP - 1081 KW - covariance KW - hypothesis-testing KW - statistics AU - Ledoit, Olivier AU - Wolf, Michael PY - 2002/// UR - http://dx.doi.org/10.2307/1558696 ER -