Large Sample Covariance Matrices and High-Dimensional Data Analysis

Download or read book Large Sample Covariance Matrices and High-Dimensional Data Analysis written by Jianfeng Yao and published by Cambridge University Press. This book was released on 2015-03-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 first-hand 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.