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＜E-Book＞
Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference / by Zheng Gao, Stilian Stoev
(SpringerBriefs in Probability and Mathematical Statistics. ISSN:23654341)

Edition	1st ed. 2021.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2021
Language	English
Size	XIII, 140 p. 12 illus., 2 illus. in color : online resource
Authors	*Gao, Zheng author Stoev, Stilian author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Stochastic processes LCSH:Statistics  FREE:Probability Theory FREE:Stochastic Processes FREE:Statistics
Notes	Chapter 1 Introduction and Guiding Examples -- Chapter 2 Risks, Procedures, and Error Models -- Chapter 3 A Panorama of Phase Transitions -- Chapter 4 Exact Support Recovery Under Dependence -- Chapter 5 Bayes and Minimax Optimality -- Chapter 6 Uniform Relative Stability for Gaussian Array -- Chapter 7 Fundamental Statistical Limits in Genome-wide Association Studies -- References -- Additional proofs -- Exact support recovery in non AGG models This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors. HTTP:URL=https://doi.org/10.1007/978-3-030-80964-5

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