Abstract: In this paper we consider the problem of constructing confidence intervals in the presence of nuisance parameters. We discuss a generalization of the unified method of Feldman and Cousins (1998) with nuisance parameters. We demonstrate our method with several examples that arise frequently in High Energy Physics and Astronomy. We also discuss the hybrid resampling method of Chuang and Lai (1998, 2000), and implement it in some of the problems.
Key words and phrases: Confidence intervals, EM algorithm, hybrid resampling method, mixture distribution, profile likelihood, signal and noise.