Normal Approximation and Asymptotic Expansions
Part of Classics in Applied Mathematics
- Authors:
- Rabi N. Bhattacharya, University of Arizona
- R. Ranga Rao, University of Illinois, Urbana-Champaign
- Date Published: November 2010
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
- format: Paperback
- isbn: 9780898718973
Paperback
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Although Normal Approximation and Asymptotic Expansions 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 is also 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 the necessary background on: weak convergence theory, Fourier analysis, geometry of convex sets and the relationship between lattice random vectors and discrete subgroups of Rk.
Read more- This updated edition of the book contains a chapter that provides an application of Stein's method of approximation to the multivariate CLT
- 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
- Appropriate for both graduate students and researchers
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×Product details
- Date Published: November 2010
- format: Paperback
- isbn: 9780898718973
- length: 332 pages
- dimensions: 228 x 152 x 17 mm
- weight: 0.46kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface to the Classics Edition
Preface
1. Weak convergence of probability measures and uniformity classes
2. Fourier transforms and expansions of characteristic functions
3. Bounds for errors of normal approximation
4. Asymptotic expansions-nonlattice distributions
5. Asymptotic expansions-lattice distributions
6. Two recent improvements
7. An application of Stein's method
Appendix A.1. Random vectors and independence
Appendix A.2. Functions of bounded variation and distribution functions
Appendix A.3. Absolutely continuous, singular, and discrete probability measures
Appendix A.4. The Euler–MacLaurin sum formula for functions of several variables
References
Index.
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