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.
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