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Power of Certain Multivariate Normal Tests Based on Likelihood Ratio Test with Unknown Covariance Matrix

Tsunehisa Imada, Hideyuki Douke

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Abstract

We discuss the power of a certain multivariate one-sided test and a certain multivariate two-sided test for normal mean vectors based on the likelihood ratio test under the assumption that the covariance matrix is unknown.We calculate the power by using conservative critical values for a specified significance level derived by upper bounds of the distributions of the likelihood ratio test statistics.We give some numerical examples regarding critical values and power of the test.

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We discuss the power of a certain multivariate one-sided test and a certain multivariate two-sided test for normal mean vectors based on the likelihood ratio test under the assumption that the covariance matrix is unknown.We calculate the power by using conservative critical values for a specified significance level derived by upper bounds of the distributions of the likelihood ratio test statistics.We give some numerical examples regarding critical values and power of the test.

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Available abstract

We discuss the power of a certain multivariate one-sided test and a certain multivariate two-sided test for normal mean vectors based on the likelihood ratio test under the assumption that the covariance matrix is unknown.We calculate the power by using conservative critical values for a specified significance level derived by upper bounds of the distributions of the likelihood ratio test statistics.We give some numerical examples regarding critical values and power of the test.

Key concepts: Covariance matrix, Statistics, Estimation of covariance matrices, Multivariate statistics, Multivariate normal distribution, Mathematics, Likelihood-ratio test, Scatter matrix

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