不同自变量的变系数模型的估计

讨论具有不同自变量的变系数模型的函数系数的估计及其大样本性质。使用局部线性方法和积分方法,得到函数系数的积分估计;由于该估计有较大的方差,进一步使用回切法改进这一估计,获得了函数系数的改进估计;同时,研究了改进估计的渐近正态性。最后,用模拟例子说明提出的估计方法是有效的。

ESTIMATION OF VARYING-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In the paper, the varying-coefficient regression models with different smoothing variables in different coefficient functions are discussed. First, the integrated estimates of the coefficient functions are given by integrating the sample on the initial value obtained by local linear technique. Then, the improvement estimates of the coefficient functions are proposed by a one-step back-fitting procedure on the integrated estimates. The improvement estimators share the same asymptotic normalities as the local linear estimators for the varying coefficient models with a single smoothing variable in different functions. Finally the simulation example shows that the procedure is effective.