Cambridge Series in Statistical and Probabilistic Mathematics : Large Sample Covariance Matrices and High-Dimensional Data Analysis Series Number 39 Hardback

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.