Controlling the bias is central to estimating semiparametric models. Many methods have been developed to control bias in estimating conditional expectations while maintaining a desirable variance order. However, these methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, nonoptimal windows are selected with undersmoothing needed to ensure the appropriate 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.

控制偏差是估计半参数模型的核心。已经开发了许多方法来控制估计条件期望的偏差，同时保持理想的方差顺序。然而，这些方法通常在中等样本量下表现不佳。此外，也许与它们的性能有关，选择非最佳窗口时需要进行欠平滑，以确保适当的偏置顺序。在本文中，我们提出了一种用于条件期望的递归差分估计器。当该方法与针对半参数期望导数的偏差控制相结合时，我们能够在最佳窗口下获得渐近正态性。正如递归结构所表明的，在各种三重索引设计中，所提出的偏差控制在中等样本大小时比常规或高阶核和局部多项式表现得更好。