Abstract
In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies.
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This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.
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Seidel, W., Ševčíková, H. Types of likelihood maxima in mixture models and their implication on the performance of tests. Ann Inst Stat Math 56, 631–654 (2004). https://doi.org/10.1007/BF02506480
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DOI: https://doi.org/10.1007/BF02506480