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The likelihood ratio test for homogeneity in bivariate normal mixtures. (English) Zbl 1085.62075

Summary: This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in a bivariate normal mixture model with known covariance. The asymptotic null distribution of the likelihood ratio statistic and a modified likelihood ratio statistic are obtained in explicit form. The distributions are identical. The results of a small simulation study to approximate the null distribution are presented.

MSC:

62H15 Hypothesis testing in multivariate analysis
62F05 Asymptotic properties of parametric tests
62E20 Asymptotic distribution theory in statistics
62H10 Multivariate distribution of statistics
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