Detection of Sparse Mixtures: Higher Criticism and Scan Statistic
Statistics Theory
2018-02-27 v1 Statistics Theory
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.
Cite
@article{arxiv.1802.08715,
title = {Detection of Sparse Mixtures: Higher Criticism and Scan Statistic},
author = {Ery Arias-Castro and Andrew Ying},
journal= {arXiv preprint arXiv:1802.08715},
year = {2018}
}