| A semiparametric regression model is studied, where two regression curves are related through linear transformations of the data. Hardle and Marron (1990) introduced this model and derived a n -consistent estimator for the parameters of the linear transformations with fixed covariates. Kneip and Engel (1995) also studied this model, and derived a n -consistent estimator when the covariates are randomly distributed. In this paper we discuss efficiency criteria in regression models and, using a procedure outlined by Schick (1993), derive an efficient estimator for the parameters of the linear transformations of this model with random covariates. In the process, nonparametric estimators of the underlying regression function and its derivative are also derived, using locally-weighted least squares techniques. |
