缺失数据下半参数空间自回归模型的估计  

Estimation of Semiparametric Spatial Autoregressive Model with Missing Data

作　　者：马万霞 吴密霞[1] 罗国旺 Wan Xia MA;Mi Xia WU;Guo Wang LUO(School of Statistics and Data Science,Faculty of Science,Beijing University of Technology,Beijing 100124,P.R.China;College of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang550025,P.R.China)

机构地区：[1]北京工业大学理学部统计与数据科学系,北京100124 [2]贵州财经大学数学与统计学院,贵阳550025

出　　处：《数学学报（中文版）》2023年第6期1031-1044,共14页Acta Mathematica Sinica：Chinese Series

基　　金：贵州省普通高等学校青年科技人才成长项目(黔教合KY字[2022]211号)。

摘　　要：本文研究了响应变量随机缺失时部分线性空间自回归模型的估计问题.结合B样条方法,我们给出了该模型参数部分和非数部分的极大似然估计的EM算法、伪限制极大似然估计的EM算法、以及边际极大似然估计算法,并通过数值模拟比较了三种估计和相应算法在不同的样本容量、缺失比例及空间权重矩阵下数值表现.最后,通过一个实际例子进一步验证三种方法的优良性.In this paper,we study the estimation of the partial linear spatial autoregressive model with the response variable missing at random.Based on the nonparametric B-spline method,the marginal maximum Likelihood estimation and the EM algorithms for the maximum Likelihood estimation and the pseudo-restricted maximum Likelihood estimation are proposed,respectively.Numerical simulations are carried out under different sample sizes,missing rates and spatial weight matrix settings to compare the performances of the three methods.Finally,the effectiveness of the three estimation methods are verified by a real data analysis.

关 键 词：空间自回归 缺失数据 EM算法 样条逼近 似然方法 

分 类 号：O212[理学—概率论与数理统计]