Abstract
AMS 2000 subject classifications: 62G08 62G20 62M20 68Q32 62H12 Keywords: Conditional quantile regression Functional covariate Iterative reweighted least squares Reproducing kernel Hilbert space Support vector machine a b s t r a c t The topic of this paper is related to quantile regression when the covariate is a function. The estimator we are interested in, based on the Support Vector Machine method, was introduced in Crambes et al. (2011) [11]. We improve the results obtained in this former paper, giving a rate of convergence in probability of the estimator. In addition, we give a practical method to construct the estimator, solution of a penalized L 1-type minimization problem, using an Iterative Reweighted Least Squares procedure. We evaluate the performance of the estimator in practice through simulations and a real data set study.