Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions
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.
Volume (Year): 81 (2011)
Issue (Month): 12 ()
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- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731.
- Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
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