High-Dimensional Covariance Matrix Estimation

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

Auteur

Aygul Zagidullina received her Ph.D. in Quantitative Economics and Finance from the University of Konstanz, Germany, with a specialization in the areas of financial econometrics and statistical modeling. Her research interests include estimation of high-dimensional covariance matrices, machine learning, factor models and neural networks.

Contenu

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.