Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference
Published on 7. September 2021
XIII, 140 pages
978-3-030-80964-5 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2021
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
XIII, 140 p. 12 illus., 2 illus. in color.
File size
2,82 MB
ISBN-13
978-3-030-80964-5 (9783030809645)
DOI
10.1007/978-3-030-80964-5
Schweitzer Classification
Other editions
Additional editions
Zheng Gao | Stilian Stoev
Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference
Book
09/2021
1st Edition
Springer
€69.54
Shipment within 7-9 days
Persons
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.
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.
Content
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.
