Testing for complete independence in high dimensions

A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test c...

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Bibliographic Details
Published in:Biometrika 2005-12, Vol.92 (4), p.951-956
Main Author: Schott, James R.
Format: Article
Language:English
Subjects:
Alcoholism
Applications
Approximation
Biology, psychology, social sciences
Covariance matrices
Distribution theory
Exact sciences and technology
Gaussian distributions
High dimensional spaces
High-dimensional data
Hypotheses
Independence of random variables
Infinity
Mathematics
Miscellanea
Multivariate analysis
Normal distribution
Probability and statistics
Random variables
Ratio test
Sample size
Sciences and techniques of general use
Significance level
Simulation
Statistics
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Description
Summary:A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample size performance of the normal approximation is evaluated in a simulation study and the results are compared to those of the likelihood ratio test.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/92.4.951