Abstract
We consider the problem of detecting a sparse mixture as studied by Ingster (1997) and Donoho and Jin (2004). We consider a wide array of base distributions. In particular, we study the situation when the base distribution has polynomial tails, a situation that has not received much attention in the literature. Perhaps surprisingly, we find that in the context of such a power-law distribution, the higher criticism does not achieve the detection boundary. However, the scan statistic does.
Citation
Ery Arias-Castro. Andrew Ying. "Detection of sparse mixtures: higher criticism and scan statistic." Electron. J. Statist. 13 (1) 208 - 230, 2019. https://doi.org/10.1214/18-EJS1512
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