Smoothed jackknife empirical likelihood for the difference of two quantiles
The construction of confidence intervals for the difference \(\theta (p)\) of the \(p\)-th quantiles of two distribution functions based on two independent samples is studied. The traditional approach is based on the asymptotic normality of empirical estimators, which requires estimation of unknown density functions. In this paper, a smoothed estimation equation is first proposed for the difference of quantiles. Jackknife pseudo values are then defined based on this estimation equation and used to construct an empirical likelihood ratio function for \(\theta(p)\), which is shown to follow a chi-squared distribution with one degree of freedom and used to define consistent jackknife empirical likelihood (JEL) confidence intervals for \(\theta(p)\). Simulation studies are performed to compare the coverages and lengths of the JEL confidence intervals with that of confidence intervals constructed based on normal approximations.
scientific article; zbMATH DE number 6807783