Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
AbstractThis 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 non-zero 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.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 575.
Date of creation: Oct 2001
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Web page: http://www.econ.upf.edu/
Concentration asymptotics; equality test; sphericity test;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-11-27 (All new papers)
- NEP-ECM-2001-11-27 (Econometrics)
- NEP-ENT-2001-11-27 (Entrepreneurship)
- NEP-ETS-2001-11-27 (Econometric Time Series)
- NEP-NET-2001-11-27 (Network Economics)
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