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Functional linear model. (English) Zbl 0962.62081

Summary: We study a regression model in which explanatory variables are sampling points of a continuous-time process. We propose an estimator of regression by means of a functional principal components analysis analogous to the one introduced by D. Bosq [Nonparametric Functional Estimation and Related Topics, NATO ASI Ser. Ser. C 335, 509-529 (1991; Zbl 0737.62032)] in the case of Hilbertian AR processes. Both convergence in probability and almost sure convergence of this estimator are stated.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J99 Linear inference, regression
62H25 Factor analysis and principal components; correspondence analysis

Citations:

Zbl 0737.62032

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References:

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