变系数模型的核权二次推断函数方法

Kernel Quadratic Inference Function Method for Varying coefficient Model

摘要:

利用二次推断函数的思想，以一系列基矩阵的线性组合来逼近工作相关矩阵，建立了纵向数据变系数模型的核权二次推断函数（QIF），基于此得到函数系数的局部线性估计，并证明了估计的渐近性质.实际中样本量和适合的窗宽并不能保证独立结构拟合的核估计总是最好的，通过适当扩大窗宽，在局部范围内引入样本相关性，既可以提高估计的效果，又不会造成“过拟合”的现象.模拟中也给出了一种选取QIF窗宽的一种实用方法.

Abstract:

Following the idea of the quadratic inference function (QIF), a kernel quadratic function method for varying coefficient model with longitudinal data was proposed by using local polynomial smoothing method and approximating the working correlation with a serious of basic matrices in the generalized estimation equation. The asymptotic normality of the estimators of the coefficient functions was proved. This method improved the performance of the estimators by widening the bandwidth in order to plug in the correlation within subjects to the local area, which won’t lead to an “over fitting” phenomenon. An applied method was also proposed to choose QIF bandwidth in the simulation.