HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Conditional quantile estimation through optimal quantization

Abstract : In this paper, we use quantization to construct a nonparametric estimator of conditional quantiles of a scalar response Y given a d-dimensional vector of covariates X. First we focus on the population level and show how optimal quantization of X, which consists in discretizing X by projecting it on an appropriate grid of N points, allows to approximate conditional quantiles of Y given X. We show that this approximation is arbitrarily good as N goes to infinity and provide a rate of convergence for the approximation error. Then we turn to the sample case and define an estimator of conditional quantiles based on quantization ideas. We prove that this estimator is consistent for its fixed-N population counterpart. The results are illustrated on a numerical example. Dominance of our estimators over local constant/linear ones and nearest neighbor ones is demonstrated through extensive simulations in the companion paper Charlier et al. (2014).
Document type :
Journal articles
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

Contributor : Isabelle Charlier Connect in order to contact the contributor
Submitted on : Thursday, January 22, 2015 - 5:50:29 PM
Last modification on : Thursday, January 20, 2022 - 5:31:42 PM
Long-term archiving on: : Friday, September 11, 2015 - 8:35:23 AM


Article 1 revision.pdf
Files produced by the author(s)




Isabelle Charlier, Davy Paindaveine, Jérôme Saracco. Conditional quantile estimation through optimal quantization. Journal of Statistical Planning and Inference, Elsevier, 2015, 156, pp.14 - 30. ⟨10.1016/j.jspi.2014.08.003⟩. ⟨hal-01108482⟩



Record views


Files downloads