Papaspiliopoulos, Omiros and Sermaidis, Giorgos (2007) Monotonicity properties of the Monte Carlo EM algorithm and connections with simulated likelihood. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

In this note we show that the Monte Carlo EM algorithm, appropriately constructed with importance re-weighting, monotonically increases a corresponding simulated likelihood. This is result is formally proved but also intuitively explained by a formulation of the problem using auxiliary variables.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Monte Carlo method, Monotonic functions, Missing observations (Statistics)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2007
Volume:	Vol.2007
Number:	No.24
Number of Pages:	5
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Greek State Scholarship Foundation (IKY)
References:	Beskos, A., Papaspiliopoulos, O. & Roberts, G. O. (2007). Monte Carlo max- imum likelihood estimation for discretely observed di®usion processes. Ann. Statist. To appear. Chan, K. S. & Ledolter, J. (1995). Monte Carlo EM estimation for time series models involving counts. J. Amer. Statist. Assoc. 90 242{252. Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39 1{38. With discussion. Fort, G. & Moulines, E. (2003). Convergence of the Monte Carlo expectation maxi- mization for curved exponential families. Ann. Statist. 31 1220{1259. Geyer, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calcula- tions. J. Roy. Statist. Soc. Ser. B 56 261{274. Jank, W. (2006). The EM algorithm, its stochastic implementation and global optimization: Some challenges and opportunities for OR. Available from http://www.smith.umd.edu/faculty/wjank/GA-EM-SaulGass.pdf. Levine, R. A. & Casella, G. (2001). Implementations of the Monte Carlo EM algo- rithm. J. Comput. Graph. Statist. 10 422{439. McCulloch, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc. 92 162{170. Quintana, F., Liu, J. & del Pino, G. (1999). Monte Carlo EM with importance reweighting and its applications in random e®ects models. Computational Statistics & Data Analysis 29 429{444. Wei, G. C. G. & Tanner, M. A. (1990). A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Amer. Statist. Assoc. 85 699{704. Wu, C. F. J. (1983). On the convergence properties of the EM algorithm. Ann. Statist. 11 95{103.
URI:	http://wrap.warwick.ac.uk/id/eprint/35557

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