Multivariate statistics: high-dimensional and large-sample approximations

This timely book provides comprehensive coverage of a topic that has not beenadequately covered in existing multivariate books. Recently developed resultsare presented in addition to thorough coverage of high-dimensional data analysis. Several challenging problems still need to be tackled in the area of multivariate analysis, and one recent problem stems from the fact that the large sample approximations worsen as the dimension p increases in comparison with the sample size n. As detailed in this book, one way of overcoming this difficulty is to study approximations that are under the high-dimensional framework. Such high-dimensional approximations have shown to work well in the low dimensional case (p=5, n=50) as well as in the high-dimensional case (p=30, n=50). Existing books on multivariate analysis tend to restrict themselves to the discussion on statistical results based on large sample approximations only; however, recent data has created a situation when the dimension p exceeds the samplesize n. Another problem concerns the error estimate of asymptotic approximations since most results only supply the order estimate. However, such estimatesdo not provide information on actual errors for given n, p, and parameters. This book addresses this issue by providing computable error bounds in additionto order estimates. High-dimensional asymptotic distributions and sample asymptotic distributions are provided, and computable error bounds for large sample and high-dimensional approximations are discussed. Bootstrap methods are also discussed for theoretical accuracy.

• ISBN: 978-0-470-41169-8
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 568
• Fecha Publicación: 12/02/2010
• Nº Volúmenes: 1
• Idioma: Inglés