Nonparametric likelihood ratio confidence intervals

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 empiri cal likelihood. The approach enjoys the same asymptotic:properties as empir ical likelihood, but is analytically and computationally less cumbersome. T he simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as a means of reducing coverage error to levels c omparable with those obtained by more computationally-intensive techniques such as the iterated bootstrap. A simulation study confirms that coverage e rror may be substantially reduced by simple analytic adjustment of the nonp arametric likelihood interval and that bootstrapping the distribution of th e nonparametric likelihood ratio results in very desirable coverage accurac y.