Computing Extended Maximum Likelihood Estimates for Linear Parameter Models

Abstract

SUMMARY Methods are given for computing extended maximum likelihood estimates in which one or more parameter estimates are infinite at the supremum of the likelihood. The results are given for a broad class of regression-like models based on independent observations with linearly related parameters including, in particular, the generalized linear models. The estimation consists of two steps: A linear programming step to identify the infinite components and a more conventional function optimization step to optimize the remaining finite components. Provision is made for nuisance parameters. Two algorithms are presented and examples illustrating their use are given.