Sieve least squares estimation for partially nonlinear models

This paper considers a partially nonlinear model E(Y|X,T)=H(βTX)+g(T), which is a sub-model of the general partially nonlinear model but has some particular advantages in statistical inference. We develop a sieve least squares method to estimate the parameters of the parametric part and the nonparametric part. The consistency and asymptotic normality of the estimator for the parametric part are established. Simulation results show that the sieve estimators perform quite well.