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

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.

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.

DOI : https://doi.org/10.1214/10-AIHP384
Classification:  60G50,  60F05
Keywords: normal and Poisson approximations, zero bias transformation, Stein's method, reverse Taylor formula, concentration inequality
@article{AIHPB_2012__48_1_258_0,
     author = {Jiao, Ying},
     title = {Zero bias transformation and asymptotic expansions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {1},
     year = {2012},
     pages = {258-281},
     doi = {10.1214/10-AIHP384},
     zbl = {1238.60050},
     mrnumber = {2919206},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2012__48_1_258_0}
}
Jiao, Ying. Zero bias transformation and asymptotic expansions. Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 1, pp. 258-281. doi : 10.1214/10-AIHP384. http://www.numdam.org/item/AIHPB_2012__48_1_258_0/

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