Description

Book Synopsis
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.

Table of Contents

Foreword.- 1 Introduction.- 2 Traditional Estimators and Standard Asymptotics.- 3 Finite Sample Performance of Traditional Estimators.- 4 Traditional Estimators and High-Dimensional Asymptotics.- 5 Summary and Outlook.- Appendices.

High-Dimensional Covariance Matrix Estimation: An Introduction to Random Matrix Theory

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    A Paperback by Aygul Zagidullina

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      View other formats and editions of High-Dimensional Covariance Matrix Estimation: An Introduction to Random Matrix Theory by Aygul Zagidullina

      Publisher: Springer Nature Switzerland AG
      Publication Date: 30/10/2021
      ISBN13: 9783030800642, 978-3030800642
      ISBN10: 3030800644
      Also in:
      Business, Finance & Law Econometrics and economic statistics Computing Databases / Data management Mathematics Probability and statistics

      Description

      Book Synopsis
      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.

      Table of Contents

      Foreword.- 1 Introduction.- 2 Traditional Estimators and Standard Asymptotics.- 3 Finite Sample Performance of Traditional Estimators.- 4 Traditional Estimators and High-Dimensional Asymptotics.- 5 Summary and Outlook.- Appendices.

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