中文摘要：

提出了一种变系数模型的减小方差估计。在任意估计点,利用其附近3个点的局部线性估计的线性组合得到减小方差估计。所得估计与局部线性估计有相同的渐近条件偏差,但较局部线性估计有更小的渐近条件方差,而且该估计具有局部线性估计的良好性质,局部线性估计所采用的窗宽选取方法均可直接应用于该估计。通过数值模拟计算,表明所提出的方法在有限样本下也可以有效地降低估计方差。

英文摘要：

A variance reduction method for varying-coefficient models is proposed. At any point of estimation,we define a variance-reduced estimator as a linear combination of local linear estimators at three nearby points. The resulting estimator retains the same asymptotic conditional bias as the local linear estimator and has smaller asymptotic conditional variance. Furthermore,the variance-reduced estimator retains many advantages of the local linear estimator,and bandwidth selection procedures are straightforward given those for local linear regression. Simulation studies are performed which demonstrate the efficacy of our variance reduction methods in finite sample settings.