Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models |
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Authors: | Nadine Hilgert Bruno Portier |
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Affiliation: | 1. UMR 729 MISTEA, INRA SupAgro, 2 Place Viala, 34060, Montpellier Cedex, France 2. LMI EA 3226, INSA de Rouen, BP 08, Avenue de 1??Universit??, 76800, Saint-Etienne du Rouvray, France
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Abstract: | 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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