Normal Approximation and Asymptotic Expansions

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). 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.

Preface to the Classics Edition Preface Chapter 1: Weak Convergence of Probability Measures and Uniformity Classes Chapter 2: Fourier Transforms and Expansions of Characteristic Functions Chapter 3: Bounds for Errors of Normal Approximation Chapter 4: Asymptotic Expansions-Nonlattice Distributions Chapter 5: Asymptotic Expansions-Lattice Distributions Chapter 6: Two Recent Improvements Chapter 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.