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Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference de Zheng Gao

Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference: SpringerBriefs in Probability and Mathematical Statistics

Autor Zheng Gao, Stilian Stoev
en Limba Engleză Paperback – 8 sep 2021
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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Specificații

ISBN-13: 9783030809638
ISBN-10: 3030809633
Pagini: 140
Ilustrații: XIII, 140 p. 12 illus., 2 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.23 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Probability and Mathematical Statistics

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

Zheng Gao graduated with a PhD in Statistics from the University of Michigan in 2020. His research focuses on large-scale multiple testing problems and real-time anomaly detection on high-dimensional data streams.

Stilian Stoev is a Full Professor of Statistics at the University of Michigan, Ann Arbor. His research involves topics in applied probability, statistics and their applications to insurance and computer networks. Most recently, he has been working on extreme value theory.

Caracteristici

Provides a unified exposition of fundamental problems in high-dimensional statistics Tackles canonical problems of detection and support estimation for sparse signals observed with noise Gives an application to statistical genetics