Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference / by Zheng Gao, Stilian Stoev.

Format:

Book

Author/Creator:

Gao, Zheng, author.

Stoev, Stilian, author.

Series:

SpringerBriefs in Probability and Mathematical Statistics, 2365-4341

Language:

English

Subjects (All):

Probabilities.

Stochastic processes.

Statistics.

Probability Theory.

Stochastic Processes.

Local Subjects:

Probability Theory.

Stochastic Processes.

Statistics.

Physical Description:

1 online resource (147 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

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. .

Contents:

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.

Notes:

Print version record.

ISBN:

3-030-80964-1

OCLC:

1267762347