Acceleration of the EM and ECM algorithms using the Aitken δ 2 method for log-linear models with partially classified data

In this paper, we discuss the MLEs for log-linear models with partially classified data. We propose to apply the Aitken δ 2 method of Aitken [Aitken, A.C., 1926. On Bernoulli’s numerical solution of algebraic equations. Proc. R. Soc. Edinburgh 46, 289–305] to the EM and ECM algorithms to accelerate...

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Bibliographic Details
Published inStatistics & probability letters Vol. 78; no. 15; pp. 2332 - 2338
Main Authors Kuroda, Masahiro, Sakakihara, Michio, Geng, Zhi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2008
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ISSN0167-7152
1879-2103
DOI10.1016/j.spl.2008.01.102

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Summary:In this paper, we discuss the MLEs for log-linear models with partially classified data. We propose to apply the Aitken δ 2 method of Aitken [Aitken, A.C., 1926. On Bernoulli’s numerical solution of algebraic equations. Proc. R. Soc. Edinburgh 46, 289–305] to the EM and ECM algorithms to accelerate their convergence. The Aitken δ 2 accelerated algorithm shares desirable properties of the EM algorithm, such as numerical stability, computational simplicity and flexibility in interpreting the incompleteness of data. We show the convergence of the Aitken δ 2 accelerated algorithm and compare its speed of convergence with that of the EM algorithm, and we also illustrate their performance by means of a simulation.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2008.01.102