Zero bias transformation and asymptotic expansions
Jiao, Ying
Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012), p. 258-281 / Harvested from Numdam
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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.

Publié le : 2012-01-01
DOI : https://doi.org/10.1214/10-AIHP384
Classification:  60G50,  60F05 
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     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {48},
     year = {2012},
     pages = {258-281},
     doi = {10.1214/10-AIHP384},
     mrnumber = {2919206},
     zbl = {1238.60050},
     language = {en},
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Jiao, Ying. Zero bias transformation and asymptotic expansions. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) pp. 258-281. doi : 10.1214/10-AIHP384. http://gdmltest.u-ga.fr/item/AIHPB_2012__48_1_258_0/

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