Normal Approximation and Asymptotic Expansions (Probability & Mathematical Statistics S.) - Hardcover

Bhattacharya, Rabindranath; Rao, Ramaswamy Ranga

Hardcover

ISBN 10: 047107201X ISBN 13: 9780471072010

Publisher: John Wiley & Sons Inc, 1976

Synopsis

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.

About this title

Book Description

An important book for statisticians due to both its treatment of various refinements of the multivariate central limit theorem and its exposition of asymptotic expansions. It is appropriate for graduate students of statistics and probability, as well as researchers whose work involves the asymptotic theory of statistics.

About the Author

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.

Edition details

• Publisher: John Wiley & Sons Inc
• Publication date: 1976
• Language: English
• ISBN 10: 047107201X
• ISBN 13: 9780471072010
• Binding: Hardcover
• Number of pages: 288