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

Small-sample properties of a nonparametric estimator of conditional quantiles based on optimal quantization, that was recently introduced (J. Statist. Plann. Inference, 156, 14–30, 2015), are investigated. More precisely, (i) the practical implementation of this estimator is discussed (by proposing in particular a method to properly select the corresponding smoothing parameter, namely the number of quantizers) and (ii) its finite- sample performances are compared to those of classical competitors. Monte Carlo studies reveal that the quantization-based estimator competes well in all cases and sometimes dominates its competitors, particularly when the regression function is quite complex. A real data set is also treated. While the main focus is on the case of a univariate covariate, simulations are also conducted in the bivariate case