Testing the Order of a Normal Mixture in Mean

Abstract

There has been a rapid progress in designing valid and effective statistical hypothesis tests for the order of a finite mixture model. In particular, EM-test for the order of the mixture model has been developed and found effective when the component distribution contains a single parameter. EM-test is found to be particularly effective and elegant for the order of normal mixture in both mean and variance. The idea behind EM-test has been found widely applicable. In this paper, we investigate the use of EM-test for the order of a finite normal mixture in the mean parameter with equal but unknown component variances. We show that for any positive integer $m_0 \ge 2,$ the limiting distribution of the EM-test for the order of $m_0$ against the higher order alternative is $\chi ^2_{m_0-1}.$ A genetic example is used to illustrate the application of the EM-test.

Keywords

EM-test / Homogeneity / Mixture model / Modified likelihood ratio test / Structural parameter

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Funding

Natural Sciences and Engineering Research Council of Canada(RGPIN-2014-03743)

Natural Sciences and Engineering Research Council of Canada(RGPIN-2015-06592)