Central limit theorem and convergence to stable laws in Mallows distance

Johnson, Oliver; Samworth, Richard

Bernoulli, Tome 11 (2005) no. 1, p. 829-845 / Harvested from Project Euclid

Résumé

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.

Publié le : 2005-10-14
Classification: central limit theorem, Mallows distance, probability metric, stable law, Wasserstein distance

@article{1130077596,
     author = {Johnson, Oliver and Samworth, Richard},
     title = {Central limit theorem and convergence to stable laws in Mallows distance},
     journal = {Bernoulli},
     volume = {11},
     number = {1},
     year = {2005},
     pages = { 829-845},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1130077596}
}

Johnson, Oliver; Samworth, Richard. Central limit theorem and convergence to stable laws in Mallows distance. Bernoulli, Tome 11 (2005) no. 1, pp.  829-845. http://gdmltest.u-ga.fr/item/1130077596/