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含缺失数据线性模型回归系数的约束EM算法 被引量：4

THE RESTRICTED EM ALGORITHM FOR REGRESSION COEFFICIENTS OF THE LINEAR MODEL WITH MISSING DATA
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摘要 应用EM算法求含缺失数据的约束线性模型回归系数的极大似然估计,该回归系数满足线性不等式约束．我们提出M-步的优化算法,并针对正态模型讨论EM序列的收敛性,最后举例说明算法的应用． The paper gives the maximum likelihood estimators of regression coefficients in the constrained linear model which have missing data by using EM algorithm, here the constraints are given by linear inequalities. We propose an optimization algorithm of M-step and discuss some convergence properties of the EM sequence for the normal model. Finally, the suggested algorithm is illustrated by a numerical example.
作者 沈启霞 刘心声
机构地区 南京航空航天大学理学院
出处 《南京大学学报（数学半年刊）》 CAS 2007年第1期122-131,共10页 Journal of Nanjing University(Mathematical Biquarterly)
关键词 缺失数据 EM算法 极大似然估计 线性不等式约束 missing data, EM algorithm, maximum likelihood estimators, linear inequalities constraints
分类号 O212.1 [理学—概率论与数理统计]
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参考文献8

  • 1Dempster A P, Laird N and Rubin D B. Maximam Likelihood Estimation from Incomplete Data via the EM Algorithm (with discussion). Journal of Royal Statistical Association B, 1977, 39: 1-38.
  • 2Kim D K and Taylor J M G. The Restricted EM Algorithm for Maximum Likelihood Estimation under Linear Restrictions on the Parameters. Journal of the American Statistical Association, 1995,430: 708-716.
  • 3Shi N Z, Zheng S R and Guo J H. The Restricted EM Algorithm under Inequality Restrictions on the Parameters. Journal of Multivariate Analysis, 2005, 92: 53-76.
  • 4Kudo A. A Multivariate Analogue of the One-sided Test. Biometrika, 1963,50: 403-418.
  • 5Dykstra R L. An Algorithm for Restricted Least Squares Regression. Journal of the American Statistical Association, 1983, 78: 837-842.
  • 6郑术蓉,史宁中,郭建华.含缺失数据线性模型的线性不等式约束EM算法[J].中国科学（A辑）,2005,35(2):231-240. 被引量：12
  • 7Kunzi H P, Krelle W and Oettli W. Nichtlineare Programmiorung. Springer-Verlag Berlin. Heicleelberg, 1962.
  • 8Louis T A. Finding the Observed Information Matrix when Using the EM Algorithm. Journal of Royal Statistical Association B, 1977, 39:1-38.

二级参考文献10

  • 1Dempster A P, Laird N M, Rubin D B. Maximum likelihood from incomplete data via the EM algorithm(with discussion). Journal of the Royal Statistical Society, Series B, 1977, 39:1-38.
  • 2Little R J A, Rubin D R. Statistical Analysis with Missing Data. New York: Wiley, 1987.
  • 3Wu C F J. On the convergence properties of the EM algorithm. The Annals of Statistics, 1983, 11: 95- 103.
  • 4Zangwill W I. Nonlinear Programming: A Unified Approach. Englewood Cliffs: Prentice Hall, 1969.
  • 5Boyles R A. On the convergence of the EM algorithm. Journal of the Royal Statistical Society, Series B,1983, 45:47-50.
  • 6Kim D K, Taylor J M G. The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters. Journal of the American Statistical Association, 1995, 430:708-716.
  • 7Dykstra R L, Robertson T, Silvapulle M J. Journal of Statistical Planning and Inference, 2002, 107(1-2).
  • 8Shi N Z, Zheng S R, Guo J H. The restricted EM algorithm under inequality restrictions on the parameters. Journal of Multivariate Analysis, 2005, 92:53-76.
  • 9Danfig G B, Eaves B C. Studies in Optimization. Washington: Mathematical Association of America,1974.
  • 10Liew C K. Inequality constrained least-squares estimation. Journal of the American Statistical Association, 1976, 71:746-751.

共引文献11

同被引文献43

引证文献4

二级引证文献18

南京大学学报（数学半年刊）
2007年 第1期

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