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Article Dans Une Revue Probability Theory and Related Fields Année : 2007

CLT in Functional Linear Regression Models

Résumé

We propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made.
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Dates et versions

hal-00007772 , version 1 (03-08-2005)

Identifiants

Citer

Hervé Cardot, André Mas, Pascal Sarda. CLT in Functional Linear Regression Models. Probability Theory and Related Fields, 2007, pp.138, 325-361. ⟨10.1007/s00440-006-0025-2⟩. ⟨hal-00007772⟩
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