Abstract:
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We study a likelihood ratio test for Gaussian mixtures. The test is based on the nonparametric maximum likelihood estimator in the context of demixing (Kiefer and Wolfowitz, 1956). We prove that when the mixing distribution is supported in [-M_n,M_n] with M_n^2\le\log n/\log9, the test is of equal or smaller order than M_n^2.
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