ABSTRACT

At the present there exists a general abstract theory for the construction of efficient estimates of the parameter of interest in a semi parametric model in the case of independent and identically distributed (iid) data. Schick ( 1986) showed how to construct efficient estimates in this case. His construction requires the availability of a preliminary Jli-consistent estimator of the parameter of interest and an appropriate estimator of the efficient score function. Klaassen (1987) showed that these conditions are also necessary. The construction given in Schick ( 1986) is not quite satisfactory from a practical point of view. It relies on a sample splitting trick and uses two estimates of the efficient score function each based on only half the sample. By imposing stronger conditions on the estimates of the efficient score function, Schick ( 1987) overcame this difficulty and was able to construct an efficient estimate that uses one estimate of the efficient score function based on the entire sample. This approach was successfully applied to semiparametric regression models in Schick ( 1993 ).