High-Dimensional Covariance Matrix Estimation
An Introduction to Random Matrix Theory
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Beschreibung
This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.
This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.
Presents random matrix theory and covariance matrix estimation under high-dimensional asymptotics Demonstrates the deficiencies of the standard statistical tools when applied in high dimensions Encourages practitioners to use the new techniques when dealing with big data problems
Autor*in
Aygul Zagidullina
Themen in »High-Dimensional Covariance Matrix Estimation«
covariance matrix estimation random matrix theory high-dimensional asymptotics high-dimensional covariance matrix estimation sample covariance matrix estimator statistical inference big data high-dimensional statistics shrinkage estimation of covariance matrices linear spectral statistics for high-dimensional inference