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.
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.
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.
