A study of the equivalence between a gauss-markoff model and its augmentation by nuisance parameters

The main purpose of this paper is to thoroughly compare a simple Gauss-Markoff model, [ULM0001], with its augmentation by nuisance parameters, [ULM0002]. The statistical objects with respect to which a comparison is carried out are: (i) the class of all estimable linear functions of main parameters y> (ii) the best linear unbiased estimator of [ULM0003]. where Qz is the orthogonal projector onto the orthogonal complement of the range of Z,