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缺失数据下多元正态模型Monte Carlo EM算法

Monte Carlo EM Algorithm for Multivariate Normal Distribution under Missing Data
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摘要 研究含有缺失数据的多元正态模型参数的极大似然估计问题,利用Monte Carlo EM算法求得多元正态模型参数的迭代解,并证明了此迭代解收敛到最优解,且其收敛速度是二阶的. Maximum likelihood estimations of the parameters of multivariate normal distribution models under missing data were studied. The iterative solution of the parameters of multivariate normal distribution models were obtained through the Monte Carlo EM algorithm and this solution converge to the optimum solution were proved and the convergence rate of this solution was secondary.
作者 王继霞 刘次华
机构地区 河南师范大学数学与信息科学学院 华中科技大学数学与统计学院
出处 《郑州大学学报（理学版）》 CAS 北大核心 2011年第3期59-61,共3页 Journal of Zhengzhou University:Natural Science Edition
基金 国家自然科学基金资助项目 编号10671057 河南省教育厅软科学研究计划 编号2010B110013
关键词 多元正态模型 缺失数据 EM算法 MONTE Carlo EM算法 Newton-Raphson算法 multivariate normal distribution missing data EM algorithm Monte Carlo EM algorithm Newton-Raphson algorithm
分类号 O212.1 [理学—概率论与数理统计]
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参考文献6

  • 1Little R J A, Rubin D R. Statistical Analysis with Missing Data[ M]. New York: Wiley, 1987.
  • 2Shi N Z,Zhong S R,Guo J H. The restricted EM algorithm under inequality restrictions on the parameters[ J]. Journal of Multivariate Analysis, 2005,92 (4) :53 - 76.
  • 3Booth J G, Hobert J P. Maximizing generalized linear mixed model likelihoods with automated Monte Carlo EM algorithm [ J ]. Journal of the Royal Statistical Society: Ser B, 1999,61 (2) :265 -285.
  • 4Dempster A P, Laird N M, Rubin D B. Maximum likelihood from incomplete data via the EM algorithm (with discussion) [ J]. Journal of the Royal Statistical Society: Ser B, 1977. 39(3) :1 -38.
  • 5罗季.Monte Carlo EM加速算法[J].应用概率统计,2008,24(3):312-318. 被引量：16
  • 6Geweke J. Bayesian inference in econometric models using Monte Carlo integration [ J]. Econometrica, 1959,57 (2):1317 - 1339.

二级参考文献8

  • 1Booth, J.G. and Hobert, J.P., Maximizing generalized linear mixed model likehoods with an automated Monte Carlo EM algotithm, Journal of the Royal Statistical Society, Ser. B, 61(1999), 265-285.
  • 2Dempster, A.P., Laird, N.M. and Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, Ser. B, 39(1977), 1-38.
  • 3Geweke, J., Bayesian inference in econometric models using Monte Carlo integration, Econometrica, 57(1989), 1317-1339.
  • 4Little, R.J.A. and Rubin, D.B., Statistical Analysis with Missing Data, New York: Wiley, 1987.
  • 5Louis T.A. Finding observed information using the EM algorithm, Journal of the Royal Statistical Society, Set. B, 44(1982), 98-130.
  • 6McLachlan, G.J. and Krishnan, T., The EM Algorithm and Extensions, New York: Wiley, 1996.
  • 7Tanner, M.A., Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, New York: Springer-Verlag, 1993.
  • 8葛勇,叶中行.不完全数据参数估计问题的算法综述与评价[J].宁夏大学学报（自然科学版）,2003,24(1):36-41. 被引量：5

共引文献15

郑州大学学报（理学版）
2011年 第3期

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