  The method of estimation in Scott and Wild (Biometrika 84 (1997) 57--71 and
J. Statist. Plann. Inference 96 (2001) 3--27) uses a reparametrization of the
profile likelihood that often reduces the computation times dramatically.
Showing the efficiency of estimators for this method has been a challenging
problem. In this paper, we try to solve the problem by investigating conditions
under which the efficient score function and the efficient information matrix
can be expressed in terms of the parameters in the reparametrized model.
