Conditional quantile estimation using optimal quantization: a numerical study

Abstract : We construct a nonparametric estimator of conditional quantiles of Y given X = x using optimal quantization. Conditional quantiles are particularly of interest when the condi-tional mean is not representative of the impact of the covariable X on the dependent variable Y . L p -norm optimal quantization is a discretizing method used since the 1950's in engineer-ing. It allows to construct the best approximation of a continuous law with a discrete law with support of size N . The aim of this work is then to use optimal quantization to construct con-ditional quantile estimators. We study the convergence of the approximation (N → ∞) and the consistency of the resulting estimator for this fixed-N approximation. This estimator was implemented in R in order to evaluate the numerical behavior and to compare it with existing methods.