L1-convergence of smoothing densities in non parametric state space models

Valérie Monbet (1) , Pierre Ailliot (2) , Pierre-François Marteau (3)

1 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192)
2 LM-Brest - Laboratoire de Mathématiques
3 VALORIA - Laboratoire de Recherche en Informatique et ses Applications de Vannes et Lorient

This paper addresses the problem of reconstructing partially observed stochastic processes. The L1 convergence of the filtering and smoothing densities in state space models is studied, when the transition and emission densities are estimated using non parametric kernel estimates. An application to real data is proposed, in which a wave time series is forecasted given a wind time series.

Mots clés: Filtering · Non parametric density estimation · Smoothing · Stability · State space models · Wind-wave models

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

Valérie Monbet, Pierre Ailliot, Pierre-François Marteau. L1-convergence of smoothing densities in non parametric state space models. Statistical Inference for Stochastic Processes, 2008, 11 (3), pp.311-325. ⟨hal-00368995⟩