Although this book was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions.
This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions. With meticulous care, the authors develop necessary background on weak convergence theory, Fourier analysis, geometry of convex sets, and the relationship between lattice random vectors and discrete subgroups of Rk. The formalism developed in the book has been used in the extension of the theory by Goetze and Hipp to sums of weakly dependent random vectors.
This edition of the book includes a new chapter that provides an application of Stein's method of approximation to the multivariate CLT.
| ISBN: | 9780898718973 |
| Publication date: | 30th September 2010 |
| Author: | R N Bhattacharya, R Ranga Rao |
| Publisher: | Society for Industrial and Applied Mathematics an imprint of SIAM - Society for Industrial and Applied Mathematics |
| Format: | Paperback |
| Pagination: | 316 pages |
| Series: | Classics in Applied Mathematics |
| Genres: |
Applied mathematics |
Although this book was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions.This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions. With meticulous care, the authors develop necessary background on weak convergence theory, Fourier analysis, geometry of convex sets, and the relationship between lattice random vectors and discrete subgroups of Rk.
Normal Approximation and Asymptotic Expansions features in the following genres: Applied mathematics
Paperback. Not Available.
Normal Approximation and Asymptotic Expansions was written by R N Bhattacharya, R Ranga Rao and published by Society for Industrial and Applied Mathematics an imprint of SIAM - Society for Industrial and Applied Mathematics
Normal Approximation and Asymptotic Expansions has 316 pages
Yes it is part of Classics in Applied Mathematics series