变系数模型的二步B样条估计

The Two-step B-spline Estimation of the Variable Coefficient Model

变系数模型(VCM)是经典线性模型的推广,其回归系数随协变量而变化。系数函数可以通过B样条估计,这产生了一步估计过程。我们展示这种一步B样条估计的方法不能在最优时不同的系数函数拥有不同的光滑度。本文使用两步估计来克服一步估计的缺点,给出两步估计的相合性,渐近正态性。模拟研究表明,在样本有限的情况下,本文的方法要比一步B样条估计更优,提高了系数函数估计的精确度。

The variable coefficient model （VCM） is the generalization of the classical linear model, and its re- gression coefficients vary with the covariate. The coefficient function can be estimated by B spline, which pro- duces a step estimation process. We show that the method of B-spline estimation can＇ t have dift^rent degrees of smoothness at optimal time. Two-step estimation was used to overcome the shortcoming of one-step estimation, and a two-step estimate of the compatibility and asymptotic normality was given. The simulation research shows that the method of this paper is better than the one-step B-spline in the case of limited sample, and improves the accuracy of the estimation of coefficient function.