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The restricted EM algorithm under inequality restrictions on the parameters

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  • Shi, Ning-Zhong
  • Zheng, Shu-Rong
  • Guo, Jianhua

Abstract

One of the most powerful algorithms for maximum likelihood estimation for many incomplete-data problems is the EM algorithm. The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters has been handled by Kim and Taylor (J. Amer. Statist. Assoc. 430 (1995) 708-716). This paper proposes an EM algorithm for maximum likelihood estimation under inequality restrictions A0[beta][greater-or-equal, slanted]0, where [beta] is the parameter vector in a linear model W=X[beta]+[var epsilon] and [var epsilon] is an error variable distributed normally with mean zero and a known or unknown variance matrix [Sigma]>0. Some convergence properties of the EM sequence are discussed. Furthermore, we consider the consistency of the restricted EM estimator and a related testing problem.

Suggested Citation

  • Shi, Ning-Zhong & Zheng, Shu-Rong & Guo, Jianhua, 2005. "The restricted EM algorithm under inequality restrictions on the parameters," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 53-76, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:53-76
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    References listed on IDEAS

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    1. Shi, N. Z., 1994. "Maximum Likelihood Estimation of Means and Variances from Normal Populations Under Simultaneous Order Restrictions," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 282-293, August.
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    4. Peter C. Wollan & Richard L. Dykstra, 1987. "Minimizing Linear Inequality Constrained Mahalanobis Distances," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 234-240, June.
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    1. Atanu Kumar Ghosh & Arnab Chakraborty, 2017. "Use of EM algorithm for data reduction under sparsity assumption," Computational Statistics, Springer, vol. 32(2), pages 387-407, June.
    2. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    3. Tian, Guo-Liang & Ng, Kai Wang & Tan, Ming, 2008. "EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4768-4778, June.

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