On the Rate of Convergence in the Multivariate CLT

F. Gotze

doi:10.1214/aop/1176990448

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Home > Journals > Ann. Probab. > Volume 19 > Issue 2 > Article

April, 1991 On the Rate of Convergence in the Multivariate CLT

F. Gotze

Ann. Probab. 19(2): 724-739 (April, 1991). DOI: 10.1214/aop/1176990448

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Abstract

Berry-Esseen theorems are proved in the multidimensional central limit theorem without using Fourier methods. An effective and simple estimate of the error in the CLT for sums and convex sets using Stein's method and induction is derived. Furthermore, the error in the CLT for multivariate functions of independent random elements is estimated extending results of van Zwet and Friedrich to the multivariate case.