Penalized Jackknife Empirical likelihood

Jackknife empirical likelihood (JEL) proposed by Jing, Yuan and Zhou (2009) is an useful approach in terms of statistical inferences, like dealing with nonliner statistics such as U-statistics. However, most contemporary problem involves high dimension model selection and the number of parameters diverges to infinity. Now we propose a penalized JEL method to solve this question, which combines JEL method with penalized empirical likelihood. The theorem is developed and shows PJEL has good properties in the consistency of variable selection and fitness of parameter estimation.