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Approximate Central Limit Theorems

Author

Listed:
  • Ben Berckmoes

    (Universiteit Antwerpen)

  • Geert Molenberghs

    (Universiteit Hasselt
    KU Leuven)

Abstract

We refine the classical Lindeberg–Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized 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 nonstandard settings in which the classical central limit theorem fails to hold. Stein’s method plays a key role in the development of this theory.

Suggested Citation

  • Ben Berckmoes & Geert Molenberghs, 2018. "Approximate Central Limit Theorems," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1590-1605, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0744-6
    DOI: 10.1007/s10959-017-0744-6
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