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Performances of a test for homogeneity against a Gaussian mixture hypothesis. (Performances d’un test d’homogénéité contre une hypothèse de mélange gaussien.) (French) Zbl 0972.62505
Summary: In this paper performances of a likelihood ratio test for testing homogeneity (i.e., no mixture) against a mixture of two distinct normal distributions with unknown means \(\theta_1\) and \(\theta_2\) and known standard deviations \(\sigma_1 =\sigma_2\) are evaluated. We follow Ghosh and Sen (1985), who proposed a locally asymptotically minimax test. Unfortunately, no tabulation was given by those authors. When \(\theta_1\) is known, a bound suggested by Davies (1977) allows one to find the approximate percentage point. With a slight modification of the test statistic we use the same value when \(\theta_1\) is unknown.

MSC:
62F03 Parametric hypothesis testing
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