Modified Likelihood and Related Methods for Handling Nuisance Parameters in the Linear Regression Model

In this paper, different approaches to dealing with nuisance parameters in the likelihood based inference are presented and illustrated by reference to the linear regression model with nonspherical errors. The estimator of the error variance using each of the approaches is also derived for the linear regression model with spherical erors. We observe that many of these estimators are unbiased. A theoretical comparison of the likelihood functions is reported and we note that some of them are equivalent.