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.
Acknowledgments
The author thanks Chao Gao for suggesting this problem, providing detailed and helpful comments on multiple drafts, and offering substantial encouragement.
Citation
Subhodh Kotekal. "Statistical limits of sparse mixture detection." Electron. J. Statist. 16 (2) 4982 - 5018, 2022. https://doi.org/10.1214/22-EJS2053
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