Gao / Stoev Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference

1. Auflage 2021
ISBN: 978-3-030-80964-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 140 Seiten

Reihe: SpringerBriefs in Probability and Mathematical Statistics

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. 

Zielgruppe

Graduate

Autoren/Hrsg.

Gao, Zheng

Stoev, Stilian

Inhaltsverzeichnis

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.

Über Autor(innen)

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.