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Quantile regression when the covariates are functions

Hervé Cardot·Christophe Crambes·Pascal Sarda
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Abstract

This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a penalized L1 type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

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Hervé Cardot, Christophe Crambes, Pascal Sarda. 2007-03-02. Quantile regression when the covariates are functions. https://arxiv.org/abs/math/0703056

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