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  3. Large Sample Covariance Matrices and High-Dimensional Data Analysis
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  • Cited by 84
Publisher:
Cambridge University Press
Online publication date:
April 2015
Print publication year:
2015
Online ISBN:
9781107588080
DOI:
https://doi.org/10.1017/CBO9781107588080
Subjects:
Computer Science, Pattern Recognition and Machine Learning, General Statistics and Probability, Statistical Theory and Methods, Statistics and Probability
Series:
Cambridge Series in Statistical and Probabilistic Mathematics (39)
Information

Book description

High-dimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that several well-known methods in multivariate analysis become inefficient, or even misleading, when the data dimension p is larger than, say, several tens. A seminal example is the well-known inefficiency of Hotelling's T2-test in such cases. This example shows that classical large sample limits may no longer hold for high-dimensional data; statisticians must seek new limiting theorems in these instances. Thus, the theory of random matrices (RMT) serves as a much-needed and welcome alternative framework. Based on the authors' own research, this book provides a firsthand introduction to new high-dimensional statistical methods derived from RMT. The book begins with a detailed introduction to useful tools from RMT, and then presents a series of high-dimensional problems with solutions provided by RMT methods.

Reviews

'This is the first book which treats systematic corrections to the classical multivariate statistical procedures so that the resultant procedures can be used for high-dimensional data. The corrections have been done by employing asymptotic tools based on the theory of random matrices.'

Yasunori Fujikoshi - Hiroshima University, Japan

'… this book is the first to cover these topics and can serve both as a good introduction to the topics as well as a comprehensive reference on the state of the art.'

Robert Stelzer Source: MathSciNet

'This book deals with the analysis of covariance matrices under two different assumptions: large-sample theory and high-dimensional-data theory. While the former approach is the classical framework to derive asymptotics, nevertheless the latter has received increasing attention due to its applications in the emerging field of big-data. Due to its novelty and its relevance in the current research, the authors focus mainly on the high-dimensional-data framework. … The theory and the applications are presented under both the large-sample theory and the high-dimensional-data theory, and thus the reader can easily appreciate the differences between the two approaches. The material is presented in a quite simple manner, and the reader only needs some pre-requisites in basic mathematical statistics, linear algebra, and theory of multivariate normal distributions. Some technical prerequisites are collected in two appendices. Therefore, the book can be used by graduate students and researchers in a wide range of disciplines, ranging from mathematics to applied sciences.'

Fabio Rapallo Source: Zentralblatt MATH

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Contents

Contents
References
References
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