Functional sliced inverse regression analysis |
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Authors: | L Ferré A F Yao |
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Institution: | 1. Université Toulouse le Mirail, Equipe GRIMM , 5, Allées Antonio Machado, Toulouse Cedex, France , 31058;2. Université Paul Sabatier, Laboratoire de Statistique et Probabilités, URMR C 5583 , 118, route de Narbonne, Toulouse Cedex, France , 31062 |
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Abstract: | Most of the usual multivariate methods have been extended to the context of functional data analysis. Our contribution concerns the study of sliced inverse regression (SIR) when the response variable is real but the regressor is a function. In the first part, we show how the relevant properties of SIR remain essentially the same in the functional context under suitable conditions. Unfortunately, the estimation procedure used in the multivariate case cannot be directly transposed to the functional one. Then, we propose a solution that overcomes this difficulty and we show the consistency of the estimates of the parameters of the model. |
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Keywords: | Functional data analysis Sliced inverse regression High dimensional data Curve estimation |
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