NONPARAMETRIC ESTIMATION OF SEMIPARAMETRIC TRANSFORMATION MODELS
针对半参数变换模型，提出一种非参数估计技术，在误差项与工具变量均值独立的假设下，证明了估计量的一致性、β̂的√N收敛速度和渐近正态性，模拟显示拟合良好。
In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form: H ( Y ) = φ ( Z ) + X ′ β + U where H , φ are unknown functions, β is an unknown finite-dimensional parameter vector and the variables ( Y , Z ) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a $\sqrt N$ -convergence rate and asymptotic normality for $\hat \beta$ can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.