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Viser: Large Sample Covariance Matrices and High-Dimensional Data Analysis
Large Sample Covariance Matrices and High-Dimensional Data Analysis
Zhidong Bai, Jianfeng Yao og Shurong Zheng
(2015)
Sprog: Engelsk
Cambridge University Press
946,00 kr.
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Detaljer om varen
- 1. Udgave
- Hardback: 322 sider
- Udgiver: Cambridge University Press (Marts 2015)
- Forfattere: Zhidong Bai, Jianfeng Yao og Shurong Zheng
- ISBN: 9781107065178
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.
1. Introduction;
2. Limiting spectral distributions;
3. CLT for linear spectral statistics;
4. The generalised variance and multiple correlation coefficient;
5. The T2-statistic;
6. Classification of data;
7. Testing the general linear hypothesis;
8. Testing independence of sets of variates;
9. Testing hypotheses of equality of covariance matrices;
10. Estimation of the population spectral distribution;
11. Large-dimensional spiked population models;
12. Efficient optimisation of a large financial portfolio.
2. Limiting spectral distributions;
3. CLT for linear spectral statistics;
4. The generalised variance and multiple correlation coefficient;
5. The T2-statistic;
6. Classification of data;
7. Testing the general linear hypothesis;
8. Testing independence of sets of variates;
9. Testing hypotheses of equality of covariance matrices;
10. Estimation of the population spectral distribution;
11. Large-dimensional spiked population models;
12. Efficient optimisation of a large financial portfolio.
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