Zero bias transformation and asymptotic expansions

Y. Jiao (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

Y. Jiao. Zero bias transformation and asymptotic expansions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2012, 48 (1), pp.258-281. ⟨10.1214/10-AIHP384⟩. ⟨hal-00705925⟩