The Annals of Probability · 1991 · 292 citations · 9 references
Mathematical ProgrammingMultivariate CltBerry-esseen TheoremsIndependent Random ElementsEngineeringApproximation TheoryStatistical InferenceStochastic GeometryMultivariate ApproximationMathematical StatisticMultivariate AnalysisStatisticsConvergence AnalysisMultivariate Functions
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.
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