Conditional Quantile Estimation Based on Optimal Quantization: from Theory to Practice

Charlier, Paindaveine, and Saracco (2014) recently introduced a nonparametric estimatorof conditional quantiles based on optimal quantization, but almost exclusively focused onits theoretical properties. In this paper, (i) we discuss its practical implementation (byproposing in particular a method to properly select the corresponding smoothing parameter,namely the number of quantizers) and (ii) we investigate how its finite-sample performancescompare with those of its classical kernel or nearest-neighbor competitors. Monte Carlostudies reveal that the quantization-based estimator competes well in all cases and tends todominate its competitors for non-uniformly distributed covariates. We also treat a real dataset. While the paper mostly focuses on the case of a univariate covariate, we also brieflydiscuss the multivariate case and provide an illustration for bivariate regressors.