Empirical likelihood based variable selection

Information criteria form an important class of model/variable selection methods in statistical analysis. Parametric likelihood is a crucial part of these methods. In some applications such as the generalized linear models, the models are only specified by a set of estimating functions. To overcome the non-availability of well defined likelihood function, the information criteria under empirical likelihood are introduced. Under this setup, we successfully solve the existence problem of the profile empirical likelihood due to the over constraint in variable selection problems. The asymptotic properties of the new method are investigated. The new method is shown to be consistent at selecting the variables under mild conditions. Simulation studies find that the proposed method has comparable performance to the parametric information criteria when a suitable parametric model is available, and is superior when the parametric model assumption is violated. A real data set is also used to illustrate the usefulness of the new method.