变系数部分线性模型的半监督估计  

Semi-Supervised Estimation for the Partially Linear Varying Coefficient Models

作　　者：田汶鑫 来鹏 TIAN Wen-xin;LAI Peng(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《数学的实践与认识》2024年第6期161-174,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11771215)。

摘　　要：针对变系数部分线性模型问题,充分利用无标签数据信息提出了一种稳健且有效的半监督估计.所提出的半监督估计方法易于实现,在大样本理论下给出其渐近性质,证明了所提出估计渐近地优于传统的仅使用标签数据的估计方法.通过蒙特卡洛数值模拟和一个实际数据问题验证了所提出估计的有限样本性质.A robust and effective semi-supervised estimation method is proposed to solve the problem of the partially linear varying coefficient model by making full use of unlabeled data information.The proposed semi-supervised estimation method is easy to implement,and its asymptotic properties are given under the large sample theory.It is proved that the proposed estimation is asymptotically superior to the traditional estimation method using only labeled data.The finite sample properties of the proposed estimates are verified by Monte Carlo numerical simulations and a real data problem.

关 键 词：变系数部分线性模型 半监督学习 截距模型 局部线性估计 

分 类 号：O212.1[理学—概率论与数理统计]