论文信息 - An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem

An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem

We provide an explanation of the main ideas underlying G\"otze's main result in using Stein's method. We also provide detailed derivations of various intermediate estimates. Curiously, we are led to a different dimensional dependence of the constant than that given G\"otze's paper. We would like to dedicate this to Charles Stein on the occasion of his 90th birthday.

Rabi Bhattacharya | Susan Holmes | R. Bhattacharya | Susan P. Holmes

[1] C. Stein. Approximate computation of expectations , 1986 .

[2] F. Götze. On the Rate of Convergence in the Multivariate CLT , 1991 .

[3] A. Barbour. Stein's method and poisson process convergence , 1988, Journal of Applied Probability.

[4] R. Rao,et al. Normal Approximation and Asymptotic Expansions , 1976 .

[5] Keith Ball. The reverse isoperimetric problem for Gaussian measure , 1993, Discret. Comput. Geom..

[6] Susan Holmes,et al. Stein's Method: Expository Lectures and Applications , 2004 .

[7] R. Bhattacharya. On the functional central limit theorem and the law of the iterated logarithm for Markov processes , 1982 .

[8] Y. Rinott,et al. On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted $U$-statistics , 1997 .

[9] V. Bentkus. On the dependence of the Berry–Esseen bound on dimension , 2003 .

[10] Rabi Bhattacharya,et al. Stochastic processes with applications , 1990 .

[11] Susan P. Holmes. Stein’s method for birth and death chains , 2004 .