Normal Approximation and Asymptotic Expansions
Rabi N. Bhattacharya, R. Ranga Rao · Society for Industrial and Applied Mathematics eBooks · 2010
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.