Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions |
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Authors: | Christophe Crambes Ali Gannoun Yousri Henchiri |
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Institution: | aInstitut de Mathématique et de Modélisation de Montpellier, UMR CNRS 5149, Equipe de Probabilités et Statistique, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex, France |
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Abstract: | This paper deals with a nonparametric estimation of conditional quantile regression when the explanatory variable X takes its values in a bounded subspace of a functional space X and the response Y takes its values in a compact of the space Y?R. The functional observations, X1,…,Xn, are projected onto a finite dimensional subspace having a suitable orthonormal system. The Xi’s will be characterized by their coordinates in this basis. We perform the Support Vector Machine Quantile Regression approach in finite dimension with the selected coefficients. Then we establish weak consistency of this estimator. The various parameters needed for the construction of this estimator are automatically selected by data-splitting and by penalized empirical risk minimization. |
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Keywords: | Conditional quantile regression Functional covariates Ill-conditioned inverse problem Reproducing kernel Hilbert space Support Vector Machine |
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