An Information Criteria for Order-restricted Inference

A general information criterion with a general penalty which depends on the size of samples is developed for nested and non-nested models in the context of inequality constraints. The true parameters may be defined by a specified parametric model, or a set of specified estimating functions. When the true parameters are defined by estimating functions, we use the empirical likelihood approach to construct information criterion. The consistency of the relevant detection procedures are also established. A Monte Carlo study indicates that our new criterion is effective, compared to Anraku’ (1999) information criterion, for detecting the configuration of normal means satisfying the simple order restriction.