Abstract:

To study adaptive estimators for the regression parameter we embed the usual nonlinear regression model in a semiparametric one. The parameter of interest is the finite dimensional regression parameter and the unknown density of the error distribution is the infinite dimensional nuisance parameter. In this paper the LAN property for the semiparametric nonlinear regression model is shown. Necessary conditions for the existence of an adaptive estimator are derived and a minimax theorem is given. The interpretation of the necessary conditions is the following: In the nonlinear model we need a symmetric error density. In the linear model adaption is also possible with asymmetric error density, if we have an asymptotic symmetric design.