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

作　　者：李建波 孙晶 LI Jianbo;SUN Jing(School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,221116,China;Faculty of Science and Technology,University of Macao,Macao,China)

机构地区：[1]江苏师范大学数学与统计学院,徐州221116 [2]澳门大学科技学院,澳门

出　　处：《应用概率统计》2019年第5期525-534,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金面上项目(批准号:11571148);江苏省统计学优势学科资助项目;江苏省“六大人才高峰”高层次人才项目(批准号:RJFW-038);江苏省“青蓝工程”中青年学术带头人支持项目;江苏师范大学本科教育教学教研课题(批准号:JYKTZ201907)资助

摘　　要：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.

关 键 词：缺失数据 B样条 单指标模型 

分 类 号：O212.7[理学—概率论与数理统计]