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Book Cover for: Normal Approximation and Asymptotic Expansions, Rabi N. Bhattacharya

Normal Approximation and Asymptotic Expansions

Rabi N. Bhattacharya

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.

Book Details

  • Publisher: Society for Industrial and Applied Mathematic
  • Publish Date: Nov 11st, 2010
  • Pages: 332
  • Language: English
  • Dimensions: 0.00in - 0.00in - 0.00in - 0.00lb
  • EAN: 9780898718973
  • Categories: Probability & Statistics - General

About the Author

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).
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.