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Detection of Sparse Mixtures: Higher Criticism and Scan Statistic
Ery Arias-Castro, Andrew Ying · 2018-02-24 · via math.ST updates on arXiv.org

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.

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