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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.



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Concentration of Maxima and Fundamental Limits in

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    A Paperback / softback by Zheng Gao, Stilian Stoev

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      Publisher: Springer Nature Switzerland AG
      Publication Date: 08/09/2021
      ISBN13: 9783030809638, 978-3030809638
      ISBN10: 3030809633

      Description

      Book Synopsis

      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.



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