Parametric first-order Edgeworth expansion for Markov additive functionals. Application to M-estimations.

Déborah Ferré (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The purpose of this paper is to obtain a first-order Edgeworth expansion for additive functionals, using Fourier techniques combined with the weak Nagaev-Guivarc'h spectral method. More precisely, this paper considers parametric bivariate functionals with a view to making statistical inference. Our probabilistic results are then applied to M-estimation.

Mots clés: spectral method; non-arithmeticity condition; M-estimator; V -geometrically ergodic Markov chain

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Déborah Ferré. Parametric first-order Edgeworth expansion for Markov additive functionals. Application to M-estimations.. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2015, 51 (2), pp.781-808. ⟨hal-00668894⟩