Nonparametric likelihood ratio confidence intervals

Abstract

We consider construction of two-sided nonparametric confidence intervals in a smooth function model setting. A nonparametric likelihood approach based on Stein's least favourable family is proposed as an alternative to empirical likelihood. The approach enjoys the same asymptotic properties as empirical likelihood, but is analytically and computationally less cumbersome. The simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as a means of reducing coverage error to levels comparable with those obtained by more computationally-intensive techniques such as the iterated bootstrap. A simulation study confirms that coverage error may be substantially reduced by simple analytic adjustment of the nonparametric likelihood interval and that bootstrapping the distribution of the nonparametric likelihood ratio results in very desirable coverage accuracy. Keywords: Bootstrap; Coverage; Empirical likelihood; Least favourable family; Nonparametric likelihood.