Adjusted empirical likelihood method for quantiles

Empirical likelihood (EL) was first applied to quantiles by Chen and Hall (1993, Ann. Statist., 21, 1166-1181). In this paper, we shall propose an alternative EL approach which is also some kind of the kernel method. It not only eliminates the need to solve nonlinear equations, but also is extremely easy to implement. Confidence intervals derived from the proposed approach are shown, by an nonparametric version of Wilks' theorem, to have the same order of coverage accuracy (order 1/n) as those of Chen and Hall. Numerical results are presented to compare our method with other methods.