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

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