The restricted EM algorithm under inequality restrictions on the parameters

Authors:
Ning-Zhong Shi;Shu-Rong Zheng;Jianhua Guo
Affiliations:
Department of Mathematic, Northeast Normal University, Changchun, China;Department of Mathematic, Northeast Normal University, Changchun, China and Jilin University, Changchun, China;Department of Mathematic, Northeast Normal University, Changchun, China
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 2
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EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions

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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 A0β ≥ 0, where β is the parameter vector in a linear model W = Xβ + ε and ε is an error variable distributed normally with mean zero and a known or unknown variance matrix Σ 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.