Jackknife empirical likelihood for inequality constraints on regular functionals

Empirical likelihood is effective in many different practical situations involving moment equality and/or inequality restrictions. However, in applications with nonlinear functionals of the underlying distribution, it becomes computationally more difficult to implement. We propose the use of jackknife empirical likelihood (Jing et al., 2009) to circumvent the computational difficulties with nonlinear inequality constraints and establish the chi-bar-square distribution as the limiting null distribution of the resulting empirical likelihood-ratio statistic, where a finite number of inequalities on functionals that are regular in the sense of Hoeffding (1948), defines the null hypothesis. The class of regular functionals includes many nonlinear functionals that arise in practice and has moments as a special case. To overcome the implementation challenges with this non-pivotal asymptotic null distribution, we propose an empirical likelihood bootstrap procedure that is valid with uniformity. Finally, we investigate the finite-sample properties of the bootstrap procedure using Monte Carlo simulations and find that the results are promising.