Smoothed jackknife empirical likelihood for the one-sample difference of quantiles

The one-sample quantile difference measure, which includes the interquartile range (IQR) of a given distribution, plays an important role in statistical sciences and econometrics. A jackknife empirical likelihood (JEL) method for the quantile difference is proposed using a novel smoothed nonparametric estimating equation. The asymptotic chi-square distribution for the JEL is proved and an algorithm for computing confidence intervals (CIs) is presented. Extensive simulation results demonstrate that JEL CIs have better coverage probability and interval length compared with CIs generated by classical empirical likelihood and normal approximation methods in most cases. The US Census Bureau's Current Population Survey data set is used to illustrate the trends in household income inequality.