Section: New Results

Conditional Quantile Estimationthrough Optimal Quantization

Participants : Jérôme Saracco, Isabelle Charlier.

This work is in collaboration with Davy Paindaveine (Univ. Libre de Bruxelles).

In this work, we construct a nonparametric estimator of conditional quantiles of $Y$ given $X$ via optimal quantization. In a first step, we propose to approximate conditional quantiles thanks to optimal quantization in ${\text{L}}^p$-norm, consisting in discretizing $X$ and $Y$ thanks to some optimal grids of size $N$. We state a result of convergence of this approximation toward the true conditional quantile. The estimator was implemented in R in order to evaluate its numerical behavior and to compare it with existing estimators. A simulation study illustrates the good behavior of our estimator. The practical choice of $N$ is discussed. We apply our approach to a real data set.

This work was presented in a national conference [35] .