Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case

Edwards & Lauritzen (2001) have recently proposed the TM algorithm for finding the maximum likelihood estimate when the likelihood can be truly or artificially regarded as a conditional likelihood, and the full likelihood is more easily maximised. They have presented a proof of convergence, provided that the algorithm is supplemented by a line search.In this note a simple expression, in terms of observed information matrices, is given for the convergence rate of the algorithm per se, when it converges, and the result elucidates also in which situations the algorithm will require a line search. Essentially these are cases when the full model does not adequately fit the data.