Large Sample Covariance Matrices and High-Dimensional Data Analysis

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. INDICE: 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.

• ISBN: 978-1-107-06517-8
• Editorial: Cambridge University Press
• Encuadernacion: Cartoné
• Páginas: 322
• Fecha Publicación: 26/03/2015
• Nº Volúmenes: 1
• Idioma: Inglés