Support vector machine quantile regression approach for functional data: Simulation and application studies

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...

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Bibliographic Details
Published in:Journal of multivariate analysis 2013-10, Vol.121, p.50-68
Main Authors: Crambes, Christophe, Gannoun, Ali, Henchiri, Yousri
Format: Article
Language:English
Subjects:
Artificial intelligence
Conditional quantile regression
Convergence
Estimating techniques
Functional covariate
Iterative reweighted least squares
Mathematics
Probability
Regression analysis
Reproducing kernel Hilbert space
Statistics
Studies
Support vector machine
Support vector machines
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Summary: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 L1-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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2013.06.004