Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions

Christophe Crambes, Ali Gannoun and Yousri Henchiri

Statistics & Probability Letters, 2011, vol. 81, issue 12, 1847-1858

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.

Keywords: Conditional quantile regression; Functional covariates; Ill-conditioned inverse problem; Reproducing kernel Hilbert space; Support Vector Machine (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2011.07.008

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