Approximate Central Limit Theorems
Copyright policy )Approximate Central Limit Theorems
We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg's condition. This allows us to continue to provide information in non-standard settings in which the classical central limit theorem fails to hold. Stein's method plays a key role in the development of this theory.
15 pages
- Katholieke Universiteit Leuven Belgium
- University of Antwerp Belgium
- Hasselt University Belgium
- KU Leuven Belgium
Wasserstein metric, Statistics & Probability, Wasserstein Metric, 0101 Pure Mathematics, 60F05, FOS: Mathematics, STEINS METHOD, Lindeberg-Feller central limit theorem, Lindeberg index, Science & Technology, Stein's Method, 0104 Statistics, Probability (math.PR), Central limit and other weak theorems, 4905 Statistics, Physical Sciences, 4904 Pure mathematics, Stein's method, Prokhorov metric, Kolmogorov metric; Lindeberg–Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein’s method; Wasserstein metric, Kolmogorov metric, Mathematics, Mathematics - Probability, Kolmogorov metric; Lindeberg-Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein's method; Wasserstein metric
Wasserstein metric, Statistics & Probability, Wasserstein Metric, 0101 Pure Mathematics, 60F05, FOS: Mathematics, STEINS METHOD, Lindeberg-Feller central limit theorem, Lindeberg index, Science & Technology, Stein's Method, 0104 Statistics, Probability (math.PR), Central limit and other weak theorems, 4905 Statistics, Physical Sciences, 4904 Pure mathematics, Stein's method, Prokhorov metric, Kolmogorov metric; Lindeberg–Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein’s method; Wasserstein metric, Kolmogorov metric, Mathematics, Mathematics - Probability, Kolmogorov metric; Lindeberg-Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein's method; Wasserstein metric
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