Article ID Journal Published Year Pages File Type
1152321 Statistics & Probability Letters 2011 12 Pages PDF
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 XX and the response Y   takes its values in a compact of the space Y≔RY≔R. The functional observations, X1,…,XnX1,…,Xn, are projected onto a finite dimensional subspace having a suitable orthonormal system. The XiXi’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.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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