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Abstract:
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Sparse and moderately strong signals are naturally found in many applications, e.g. covert communications, Kuiper Belt Objects. Here, sparsity refers to the situation that out of a massive data set, only a small fraction of data points contain relevant information or signal, while others are irrelevant or noise; moderately strong signals are those stronger than a typical noise, but not stronger than all of them. Sparse inference in the regime of moderate significances poses interesting new phenomenon as well as new challenges. In this talk, we introduce three recent inference tools for the proportion of signals: the Higher Criticism , the Higher Criticism , Meinshausen and Rice's confidence lower bound, and Cai, Jin, and Low's confidence lower bound. We will discuss the asymptotic behavior of these tools in detail, and also compare their strength and weakness.
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