Normal Approximation and Asymptotic Expansions

Erscheinungsjahr 2010
ISBN: 978-0-89871-897-3
Verlag: Society for Industrial & Applied Mathematics,U.S.

Buch, Englisch, 332 Seiten, Format (B × H): 153 mm x 229 mm, Gewicht: 460 g

Reihe: Classics in Applied Mathematics

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.

Autoren/Hrsg.

Bhattacharya, Rabi N.

Rao, R. Ranga

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

Rao, R. Ranga
R. Ranga Rao received his Ph.D. from the Indian Statistical Institute in 1960. He has been on the faculty of the Department of Mathematics, University of Illinois, for more than forty years. He has held a number of visiting professorships, including several at the Tata Institute of Fundamental Research, India. He is a member of the American Mathematical Society.

Bhattacharya, Rabi N.
Rabi N. Bhattacharya received his Ph.D. from the University of Chicago in 1967. He has held regular faculty positions at the University of California, Berkeley, Indiana University and the University of Arizona. He is a member of the American Mathematical Society and a Fellow of the Institute of Mathematical Statistics. He is a recipient of a Guggenheim Fellowship and an Alexander Von Humboldt Forschungspreis. Bhattacharya has co-authored a number of graduate texts and research monographs, including Stochastic Processes with Applications (with E. C. Waymire) and Random Dynamical Systems (with M. K. Majumdar).