Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models
2012
Hilgert , Nadine (INRA , Montpellier (France). UMR 0729 Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie ) | Portier , Bruno (Institut National des Sciences Appliquées, Saint-Etienne du Rouvray(France). LMI EA 3226)
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic properties of this estimator depend on the average prediction error of the functional autoregressive function. Sufficient conditions are studied to provide strong uniform consistency and asymptotic normality of the kernel density estimator.
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