AN EFFICIENT ESTIMATOR FOR THE GENERALIZED SEMILINEAR MODEL

The generalized semilinear model (GSLIM) extends the generalized linea r model by allowing the addition of an unknown smooth function to the predictor parameter, producing a semiparametric model. Some previously proposed score-based estimators for the parametric component in this model are not root n consistent. We propose efficient estimators for b oth the parametric and nonparametric components of the GSLIM. The esti mator for the parametric component is the solution to an estimated eff icient score equation and is based on recent theoretical advances in s emiparametric estimation. The estimator for the nonparametric componen t is the maximizer of an estimated penalized likelihood of the form co nsidered by Cox and O'Sullivan. A robust standard error estimate maint ains valid inference under certain model violations. An application an d simulation results are given for data with binary outcomes, using a modified generalized cross-validation algorithm to select the smoothin g parameter. Parameter and standard error estimates are within 6% of n ominal values under a range of smooth functions tested in the simulati ons.