Normal Approximation and Asymptotic Expansions

A detailed treatment of various refinements of the multivariate central limit theorem.

Rabi N. Bhattacharya (Author), R. Ranga Rao (Author)

9780898718973

Paperback / softback, published 30 September 2010

338 pages
24.6 x 17.3 x 1.7 cm, 0.481 kg

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.

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.

Subject Areas: Miscellaneous items [WZ]