Zero bias transformation and asymptotic expansions
Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 1, pp. 258-281.

Soit W une somme de variables aléatoires indépendants. On applique la transformation zéro biais pour obtenir de façon recursive des développements asymptotiques de 𝔼[h(W)] en terme d’espérances par rapport à la loi normale, ou à la loi de Poisson si les variables aléatoires sont à valeurs entières. On discute aussi les bornes des termes d’erreur.

Let W be a sum of independent random variables. We apply the zero bias transformation to deduce recursive asymptotic expansions for 𝔼[h(W)] in terms of normal expectations, or of Poisson expectations for integer-valued random variables. We also discuss the estimates of remaining errors.

DOI : 10.1214/10-AIHP384
Classification : 60G50, 60F05
Mots-clés : normal and Poisson approximations, zero bias transformation, Stein's method, reverse Taylor formula, concentration inequality 
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Jiao, Ying. Zero bias transformation and asymptotic expansions. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 1, pp. 258-281. doi : 10.1214/10-AIHP384. http://archive.numdam.org/articles/10.1214/10-AIHP384/

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