Density estimation using bootstrap quantile variance and quantile-mean covariance

Abstract

We evaluate two density estimators based on the quantile variance and the quantile-mean covariance estimated by bootstrap. We review previous developments on density estimation related to quantiles. Monte Carlo simulations for different data generating processes, sample sizes, and other parameters show that the estimators perform well in comparison to the benchmark non-parametric kernel density estimator. Some of the explored smoothing techniques present lower bias and mean integrated squared errors, which indicates that the proposed estimator is a promising strategy.