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

ABSTRACT

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.

KEYWORDS:

• Conditional quantile
• nonparametric estimation
• kernel smoothing
• bernstein polynomials

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors wish to thank the Editor, Associate Editor and anonymous referee whose comments led to significant improvements to this manuscript. In addition, M. Belalia gratefully acknowledge the research support of the Natural Sciences and Engineering Research Council of Canada (RGPIN/05496-2020).