2008/02/01 by Peter Hall, Jiashun Jin · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Blind Source Separation Techniques #Statistical Methods and Inference #math.ST #msc:62G10 #msc:62G20 #msc:62G32 #msc:62M10 #stat.TH
paper · pdf · doi:10.1214/009053607000000767
published as Annals of Statistics 2008, Vol. 36, No. 1, 381-402 · Published in at http://dx.doi.org/10.1214/009053607000000767 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/02/01 · arxiv created 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each problem can be solved by conducting a large number of simultaneous hypothesis tests, the properties of which are readily accessed under the assumption of independence. In this paper we address the case of dependent data, in the context of higher criticism methods for signal detection. Short-range dependence has no first-order impact on performance, but the situation changes dramatically under strong dependence. There, although higher criticism can continue to perform well, it can be bettered using methods based on differences of signal values or on the maximum of the data. The relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that, under strong dependence, the higher criticism statistic behaves as though the data were partitioned into very large blocks, with all but a single representative of each block being eliminated from the dataset.