| Description: |
In this paper, we study a regression model in which explanatory variables are sampling points of a continuous time process. We propose an estimate of regression by mean of a Functional Principal Component Analysis and analogous to the one introduced by Bosq (1991) in the case of Hilbertian AR processes. Both convergence in probability and almost sure convergence of this estimate are stated. Keywords : functional linear model, functional data analysis, Hilbert spaces, convergence. 1 Introduction Classical regression models, such as generalized linear models, may be inadequate in some statistical studies : it is the case when explanatory variables are digitized points of a curve. Examples can be found in different fields of application such as chemometrics (Frank and Friedman, 1993), linguistic (Hastie, Buja and Tibshirani, 1995) and many other areas (see Hastie and Mallows, 1993, and Ramsay and Silverman, 1997, among others). In this context, Frank and Friedman (1993) describe and com. |
