Empirical likelihood for linear models in the presence of nuisance parameters

Abstract

We propose a simple alternative empirical likelihood (EL) method in linear regression which requires the same conditions of the ordinary profile EL but overcomes the challenge of maximizing the likelihood in the presence of high dimensional nuisance parameters. We adapt the idea of added variable plots. We regress the response and the independent variables of main interest on the ancillary variables and construct the likelihood based on the residuals. The hence constructed EL ratio has constraints only pertaining to the parameters of interest and has a standard χ 2 limiting distribution. Numerical results are included.