In this paper we discuss a general way of improving the bias properties of nonparametric kernel regression estimators. The procedure involves choosing a parametric model and constructing a semiparametric estimator that consists of a parametric component and a nonparametric adjustment, where the parametric component is picked from the parametric model in such a way that the resulting estimator has the best bias performance. We study the method for response variables taking values in a general Hilbert space and for local linear smoother. We show that the procedure always improves the bias of the local linear estimator regardless of the choice of parametric model. We also illustrate the method via a real data example where the response variable is a random density.

在本文中，我们讨论了一种改善非参数核回归估计器偏差属性的一般方法。该过程包括选择一个参数模型，并构造一个由参数成分和非参数调整组成的半参数估计量，其中，从参数模型中选取参数成分的方式应使最终的估计量具有最佳的偏置性能。我们研究了在一般希尔伯特空间中采用值的响应变量和局部线性平滑器的方法。我们表明，无论选择何种参数模型，该程序始终可以提高局部线性估计量的偏差。我们还通过真实数据示例说明了该方法，其中响应变量是随机密度。