Statistical Limits of Sparse Mixture Detection

Subhodh Kotekal

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arXiv · 2104.02507

Statistical Limits of Sparse Mixture Detection

Subhodh Kotekal

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Abstract

We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient condition for the adaptive optimality of a Higher Criticism type testing statistic formulated by Gao and Ma. In the course of establishing these results, we offer a unified perspective through the large deviations theory. The phase transition and adaptive optimality we establish are direct consequences of the large deviation principle of the normalized log-likelihood ratios between the null and the signal distributions.

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Subhodh Kotekal. 2021-04-06. Statistical Limits of Sparse Mixture Detection. https://arxiv.org/abs/2104.02507

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