基于EM-GIBBS算法的ARMA(p,q)测量误差模型的参数估计  

Parameter Estimation of ARMA(p,q)Measurement Error Model Based on EM-GIBBS

作　　者：郑斌斌 许淑婷 李安水 张慧增 ZHENG Binbin;XU Shuting;LI Anshui;ZHANG Huizeng(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2023年第4期438-448,共11页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11901145)。

摘　　要：本文对基于ARMA(p,q)的测量误差模型的参数估计提出了EM-Gibbs算法.由于无法给出模型参数的极大似然估计解析解,本文在EM算法框架下对参数进行估计.在实施EM算法M步骤过程中,为了计算高维正态分布的隐变量一阶、二阶矩,需要求出高阶矩阵的逆矩阵.为了避开计算高阶矩阵的逆矩阵,通过Gibbs抽样,给出了隐变量的一阶、二阶矩的估计,从而给出了EM算法M步骤中参数最优值的估计.最后通过对ARMA(1,1)测量误差模型进行了数值模拟,模拟结果验证了所提EM-Gibbs算法的可行性和有效性.In this paper,the EM-Gibbs algorithm is proposed for the parameter estimation of the measurement error model based on ARMA(p,q).Since the analytic solution of the maximum likelihood estimation of model parameters cannot be given,this paper estimates the parameter under the framework of EM algorithm.In the process of EM algorithm M step,the inverse matrix of high order matrix should be obtained to calculate the first order and second order moments of hidden variables of high dimensional normal distribution.To avoid calculating the inverse matrix of the higher-order matrix,the estimation of the first-order and second-order moments of the implicit variables is given by Gibbs sampling.Then,the estimation of the optimal parameter values in the M step of the EM algorithm is provided.Finally,numerical simulation of the ARMA(1,1)measurement error model is carried out,and the simulation results verify the feasibility and effectiveness of the proposed EM-Gibbs algorithm.

关 键 词：EM算法 ARMA(p q)测量误差模型 GIBBS抽样 

分 类 号：O212.8[理学—概率论与数理统计]