Quantile regression when the covariates are functions

By Hervé Cardot, Christophe Crambes, Pascal Sarda. 2005

130 citations recorded by the source corpus.

This article 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 L 1 type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/25bbe8a34f93cbb2dd3bdf4c7cc4879ae747eeae

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Conditional quantile analysis when covariates are functions, with application to growth data (2012, methodology): “The method of Cardot et al. (2005) is an extension of the well-known quantile linear regression approach for vector covariates X , based on the estimating equation E{lα.”
The functional linear array model (2015, background): “…in the context of linear models (e.g., Reiss and Ogden, 2007; James et al., 2009), generalized linear models (e.g., Marx and Eilers, 1999; Müller and Stadtmüller, 2005; Wood, 2011; Gertheiss et al., 2013) or quantile regression models (e.g., Cardot et al., 2005; Chen and Müller, 2012a).”
Robust nonparametric estimation for functional data (2008, methodology): “[18] used a robust approach to estimate conditional quantiles of a realvalued variable and a functional covariate, seen as a linear form on a Hilbert space.”
Estimation in functional linear quantile regression (2012, background): “[7] studied smoothing splines estimators for functional linear quantile regression models, while their established rates are not sharp.”