Complete Independence in the Multivariate Normal Distribution
Testing complete independence is one of the simplest problems concerning the covariance structure of a set of measurements. A stepwise procedure proposed by Roy and Bargmann (1958) and a trace criterion due to Nagao (1973) are two well-known competitors of the likelihood ratio test of the hypothesis derived assuming the multivariate normality. We consider some modifications of the Roy-Bargmann procedure based on combinations of independent tests and find them to be asymptotically equivalent to the likelihood ratio test, which is optimal in terms of the exact slopes. The operating characteristics of various tests with samples of moderate size are examined empirically.
Key WordsCombination of tests exact slopes stepdown procedure
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