Open Access
October 2005 Central limit theorem and convergence to stable laws in Mallows distance
Oliver Johnson, Richard Samworth
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Bernoulli 11(5): 829-845 (October 2005). DOI: 10.3150/bj/1130077596


We give a new proof of the classical central limit theorem, in the Mallows (Lr-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.


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Oliver Johnson. Richard Samworth. "Central limit theorem and convergence to stable laws in Mallows distance." Bernoulli 11 (5) 829 - 845, October 2005.


Published: October 2005
First available in Project Euclid: 23 October 2005

zbMATH: 1094.60014
MathSciNet: MR2172843
Digital Object Identifier: 10.3150/bj/1130077596

Keywords: central limit theorem , Mallows distance , probability metric , Stable law , Wasserstein distance

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 5 • October 2005
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