Large Sample Covariance Matrices and High-Dimensional Data Analysis
- ISBN-10
- 1107065178
- ISBN-13
- 9781107065178
- Category
- Mathematics
- Language
- English
- Published
- 2015-03-26
- Publisher
- Cambridge University Press
- Authors
- Zhidong Bai, Jianfeng Yao, Shurong Zheng
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 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.
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