Section: New Results

Conditional quantile estimator based on optimal quantization: from theory to practice

Participants : Isabelle Charlier, Jérôme Saracco.

[21] recently introduced a promising nonparametric estimator of conditional quantiles based on optimal quantization, but almost exclusively focused on its theoretical properties. We now discuss its practical implementation (by proposing in particular a method to properly select the corresponding smoothing parameter, namely the number of quantizers) and (ii) we investigate how its finite-sample performances compare with those or classical kernel of nearest-neighbor competitors. Monte Carlo studies show that the quantization-based estimator competes well in all cases (in terms of mean squared errors) and tends to dominate its competitors as soon as the covariate is not uniformly distributed over its support. We also apply our approach to a real data set. While most of the paper focuses on the case of a univariate covariate, we also briefly discuss the multivariate case and provide an illustration for bivariate regressors. This work is in collaboration with Davy Paindaveine from Université Libre de Bruxelles. It has been presented in the national conference of the French Statistical Society of Statistics [35] and in the international conference on computational statistics [34] .