基于缺失数据的B样条单指标模型估计

B-Spline Estimation of Single Index Models with Missing Data

本文主要研究基于响应变量随机缺失的单指标模型的逆概率加权估计问题.首先通过B样条逼近未知单指标函数,然后构建逆概率加权最小二乘损失函数,接着通过两阶段牛顿迭代算法获得指标函数和指标系数的估计,最后通过大量模拟例子和实例分析说明了我们所提估计方法的有效性和合理性.

In this paper,we studied the inverse probability weighted least squares estimation of singleindex model with response variable missing at random.Firstly,the B-spline technique is used to approximate the unknown single-index function,and then the objective function is established based on the inverse probability weighted least squares method.By the two-stage Newton iterative algorithm,the estimation of index parameters and the B-spline coefficients can be obtained.Finally,through many simulation examples and a real data application,it can be concluded that the method proposed in this paper performs very well for moderate sample.