Recursive Differencing for Estimating Semiparametric Models

Controlling the bias is central to estimating semiparametric models. Many methods have been developed to control bias in estimating conditional expectations while main- taining a desirable variance order. However, these methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, non-optimal windows are selected with undersmoothing needed to ensure the appro- priate bias order. In this paper, we propose a recursive differencing estimator for conditional expectations. When this method is combined with a bias control targeting the derivative of the semiparametric expectation, we are able to obtain asymptotic normality under optimal windows. As suggested by the structure of the recursion, in a wide variety of triple index designs, the proposed bias control performs much better at moderate sample sizes than regular or higher order kernels and local polynomials.