Density Estimation using Quantile Variance and Quantile-Mean Covariance

Abstract

Based on asymptotic properties of sample Quantile Distribution derived by Hall & Martin (1988) and Ferguson (1999), we propose a novel method which explodes Quantile Variance, and Quantile-Mean Covariance to estimate distributional density from samples. The process consists in firstly estimate sample Quantile Variance and sample Quantile-Mean Covariance using bootstrap techniques and after use them to compute distributional density. We conducted Montecarlo Simulations for different Data Generating Process, sample size and parameters and we discovered that for many cases Quantile Density Estimators perform better in terms of Mean Integrated Squared Error than standard Kernel Density Estimator. Finally, we propose some smoothing techniques in order to reduce estimators variance and increase their accuracy.