Smooth estimation of conditional quantile function with mixed covariates using Bernstein polynomials

The conditional quantile function is a fundamental tool for understanding the relationship between covariates and the response variable in data analysis. In this study, we propose a novel estimator based on the Nadaraya–Watson discrete conditional distribution estimator, which uses Bernstein polynomials for smoothing. The consistency and asymptotic normality of the proposed estimator are established. Also, a simulation study to compare its performance with other existing estimators is carried out.