基于Guass-Seidel型迭代分层线性模型的参数估计  

Parameter Estimation Based on Guass-Seidel Type Iterative Hierarchical Linear Model

作　　者：周梦雨 田茂再[1,2,3] ZHOU Meng-yul;TIAN Mao-zail(School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012,China;Center for Applied Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012 [2]中国人民大学应用统计科学研究中心,北京100872 [3]中国人民大学统计学院,北京100872

出　　处：《数理统计与管理》2025年第1期135-143,共9页Journal of Applied Statistics and Management

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目(22XNL016)。

摘　　要：缺失数据现象在观测数据中是十分常见的问题,而EM算法是针对缺失数据问题中求参数估计的常用方法,将不完全数据转化为完全数据问题来处理,本文针对缺失数据的分层线性模型提出了Guass-Seidel型迭代方法,其主要思想是,迭代产生当前最新值,并运用最新值计算得到下一步最新参数估计值,对分层线性模型中固定效应与随机效应部分的参数估计进行推导,依据判断准则决定迭代过程的收敛,迭代过程结束,本文主要贡献之一在于利用Guass-Seidel型迭代提高算法收敛速度。Missing data phenomenon is a very common problem in observation data,and EM algorithm is a common method for parameter estimation in the problem of missing data,which transforms incomplete data into complete data.In this paper,a Guass-Seidel type iterative method is proposed for the Hierarchical Linear Model of missing data.The main idea is that iteration produces the current latest value,and uses the latest value to calculate the latest parameter estimation in the next step.The parameter estimation of the fixed effect and random effect part in the Hierarchical Linear Model is derived.The convergence of the iterative process is determined according to the judgment criteria,and the iteration process is finished.One of the main contributions of this paper is to improve the convergence speed of the algorithm by using the Guass-Seidel type iteration Degree.

关 键 词：缺失数据 分层线性模型 EM算法 Guass-Seidel型迭代 

分 类 号：O212[理学—概率论与数理统计]