Hall, Peter; Jin, Jiashun Properties of higher criticism under strong dependence. (English) Zbl 1139.62049 Ann. Stat. 36, No. 1, 381-402 (2008). Summary: 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. 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. Cited in 30 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 60G15 Gaussian processes Keywords:correlation; dependent data; faint information; Gaussian processes; signal detection; simultaneous hypothesis testing; sparsity × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] Anon (2005). A new method for early detection of disease outbreaks. Science Daily 23rd February. Available at http://www.sciencedaily.com/releases/2005/02/050218130731.htm. [2] Benjamini, Y. and Hochberg, Y. (1995). 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