Central limit theorem and convergence to stable laws in Mallows distance

OT Johnson, R Samworth

Research output: Contribution to journalArticle (Academic Journal)

14 Citations (Scopus)

Abstract

We give a new proof of the classical central limit theorem, in the Mallows (L-r-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality related to this metric. The key is to analyse the case where equality holds. We provide some results concerning rates of convergence. We also consider convergence to stable distributions, and obtain a bound on the rate of such convergence.
Translated title of the contributionCentral limit theorem and convergence to stable laws in Mallows distance
Original languageEnglish
Pages (from-to)829 - 845
Number of pages17
JournalBernoulli
Volume11 (5)
Publication statusPublished - Oct 2005

Bibliographical note

Publisher: Int Statistical Inst
Other identifier: IDS number 976JH

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