Titlebook: High-Dimensional Covariance Matrix Estimation; An Introduction to R Aygul Zagidullina Book 2021 The Author(s), under exclusive licence to S

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Introduction,cts of the random matrix theory. Although this matrix is commonly used in many fields of study and its properties have long been known in the context of classical statistics, recent advances in computer science and data access have revived interest in studying sample covariance matrix from the rando

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Summary and Outlook,aditional regime is the basis of classical textbooks’ statistics, while the high-dimensional regime better applies to Big Data context and closely approximates finite sample properties of standard estimators. Therefore, the objectives and contributions of this book are twofold.

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Traditional Estimators and Standard Asymptotics,We discuss the concept of a random matrix and relate it to the sample covariance matrix estimator. This short review is intended to guide the reader through the classical results.

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Finite Sample Performance of Traditional Estimators,We demonstrate that well-known multivariate statistical techniques perform poorly and become misleading, when the data dimension . is comparable in magnitude to or larger than the sample size ..

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Traditional Estimators and High-Dimensional Asymptotics,We introduce and describe various classical and modern theoretical results developed within the random matrix theory domain which are related to the covariance matrix estimation, as well as to the factor structure inference in high-dimensional data.

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Summary and Outlook,aditional regime is the basis of classical textbooks’ statistics, while the high-dimensional regime better applies to Big Data context and closely approximates finite sample properties of standard estimators. Therefore, the objectives and contributions of this book are twofold.

Allure

Aygul ZagidullinaPresents random matrix theory and covariance matrix estimation under high-dimensional asymptotics.Demonstrates the deficiencies of the standard statistical tools when applied in high dimensions.Encour

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978-3-030-80064-2The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021

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