Enhancing Quantile Function Estimation with Beta-Kernel Smoothing

This paper introduces a class of nonparametric quantile function estimators based on Beta kernel smoothing. We conduct a rigorous investigation into their large-sample properties, including asymptotic normality and mean squared equivalence to existing methods. Through extensive simulation studies, we demonstrate that the proposed Beta kernel estimators perform comparably to or outperform traditional empirical and symmetric location-scale kernel-based quantile estimators. Additionally, we provide two real-world applications to illustrate the practical effectiveness of our approach. The results suggest that Beta kernel smoothing offers a flexible and efficient alternative for quantile function estimation, particularly in cases where classical methods exhibit inefficiencies.