Abstract
We consider the problem of detecting a sparse Poisson mixture. Our results parallel those for the detection of a sparse normal mixture, pioneered by Ingster (1997) and Donoho and Jin (2004), when the Poisson means are larger than logarithmic in the sample size. In particular, a form of higher criticism achieves the detection boundary in the whole sparse regime. When the Poisson means are smaller than logarithmic in the sample size, a different regime arises in which simple multiple testing with Bonferroni correction is enough in the sparse regime. We present some numerical experiments that confirm our theoretical findings.
Citation
Ery Arias-Castro. Meng Wang. "The sparse Poisson means model." Electron. J. Statist. 9 (2) 2170 - 2201, 2015. https://doi.org/10.1214/15-EJS1066
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