Upper bounds for minimal distances in the central limit theorem
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 3, pp. 802-817.

Nous obtenons des majorations des distances minimales dans le théorème limite central pour les suites de variables aléatoires réelles indépendantes.

We obtain upper bounds for minimal metrics in the central limit theorem for sequences of independent real-valued random variables.

DOI : 10.1214/08-AIHP187
Classification : 60F05
Mots-clés : Fréchet-Dall'Aglio minimal metric, Wasserstein distance, rates of convergence, Esseen's mean central limit theorem, global central limit theorem 
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Rio, Emmanuel. Upper bounds for minimal distances in the central limit theorem. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 3, pp. 802-817. doi : 10.1214/08-AIHP187. http://www.numdam.org/articles/10.1214/08-AIHP187/

A. D. Barbour. Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Theory Related Fields 72 (1986) 289-303. | MR | Zbl

P. Bártfai. Über die entfernung der irrfahrtswege. Studia Sci. Math. Hungar. 5 (1970) 41-49. | MR | Zbl

A. Bikelis. Estimates of the remainder term in the central limit theorem. Litovsk. Mat. Sb. 6 (1966) 323-346. | MR | Zbl

I. S. Borisov, D. A. Panchenko and G. I. Skilyagina. On minimal smoothness conditions for asymptotic expansions of moments in the CLT. Siberian Adv. Math. 8 (1998) 80-95. | MR | Zbl

G. Dall'Aglio. Sugli estremi deli momenti delle funzioni di ripartizione doppia. Ann. Sc. Norm. Super Pisa Cl. Sci. 10 (1956) 35-74. | Numdam | MR | Zbl

C. G. Esseen. On mean central limit theorems. Kungl. Tekn. Högsk. Handl. Stockholm 121 (1958) 31. | MR | Zbl

M. Fréchet. Recherches théoriques modernes sur le calcul des probabilités, premier livre. Généralités sur les probabilités, éléments aléatoires. Paris, Gauthier-Villars, 1950. | MR | Zbl

M. Fréchet. Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris 244 (1957) 689-692. | MR | Zbl

I. Ibragimov. On the accuracy of Gaussian approximation to the distribution functions of sums of independent random variables. Theory Probab. Appl. 11 (1966) 559-579. | MR | Zbl

J. Komlós, P. Major and G. Tusnády. An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131. | MR | Zbl

P. Major. On the invariance principle for sums of independent identically distributed random variables. J. Multivariate Anal. 8 (1978) 487-517. | MR | Zbl

P. Massart. Strong approximation for multivariate empirical and related processes, via K.M.T. constructions. Ann. Probab. 17 (1989) 266-291. | MR | Zbl

V. V. Petrov. Sums of Independent Random Variables. Berlin, Springer, 1975. | MR | Zbl

E. Rio. Strong approximation for set-indexed partial-sum processes, via KMT constructions I. Ann. Probab. 21 (1993) 759-790. | MR | Zbl

E. Rio. Distances minimales et distances idéales. C. R. Acad. Sci. Paris 326 (1998) 1127-1130. | MR | Zbl

A. I. Sakhanenko. Estimates in the invariance principle. Proc. Inst. Math. Novosibirsk 5 (1985) 27-44. | MR | Zbl

V. M. Zolotarev. On asymptotically best constants in refinements of mean central limit theorems. Theory Probab. Appl. 9 (1964) 268-276. | MR | Zbl

V. M. Zolotarev. Metric distances in spaces of random variables and their distributions. Math. USSR Sbornik 30 (1976) 373-401. | MR | Zbl

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