Conditional quantile estimation through optimal quantization - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Statistical Planning and Inference Year : 2015

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).
Fichier principal
Vignette du fichier
Article 1 revision.pdf (809.96 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01108482 , version 1 (22-01-2015)

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook X LinkedIn More