Convergence of the Monte Carlo expectation maximization for curved exponential families

Annals of Statistics

Volumn 31, Issue 4, 2003, Pages 1220-1259

  Fort, Gersende ^a   Moulines, Eric ^b  

^a LMC   (France)

^b TELECOM PARISTECH   (France)

Author keywords

Averaging procedure; EM algorithm; Metropolis Hastings algorithms; Monte Carlo EM algorithm

Indexed keywords

EID: 0042358780     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1059655912     Document Type: Article

References (28)

1. BISCARAT, J. (1994). Almost sure convergence of a class of stochastic algorithms. Stochastic Process. Appl. 50 83-94.
2. BOOTH, J. and HUBERT, J. (1999). Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. R. Stat. Soc. Ser B Stat. Methodol. 61 265-285.
3. BRANDIÈRE, O. (1998). The dynamic system method and the traps. Adv. in Appl. Probab. 30 137-151.
4. BRÖCKER, T. (1975). Differentiable Germs and Catastrophes. Cambridge Univ. Press.
5. CAPPÉ, O., DOUCET, A., LAVIELLE, M. and MOULINES, E. (1999). Simulation-based methods for blind maximum-likelihood filter identification. Signal Processing 73 3-25.
6. CELEUX, G. and DIEBOLT, J. (1992). A stochastic approximation type EM algorithm for the mixture problem. Stochastics Stochastics Rep. 41119-134.
7. CHAN, J. and KUK, A. (1997). Maximum likelihood estimation for probit-linear mixed models with correlated random effects. Biometrics 53 86-97.
8. CHAN, K. and LEDOLTER, J. (1995). Monte Carlo EM estimation for time series models involving counts. J. Amer. Statist. Assoc. 90 242-252.
9. CHEN, H., Guo, L. and GAO, A. (1988). Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds. Stochastic Process. Appl. 27 217-231.
10. DALAL, S. and WEERAHANDI, S. (1992). Some approximations for the moments of a process used in diffusion of new products. Statist. Probab. Lett. 15 181-189.
11. DALAL, S. and WEERAHANDI, S. (1995). Estimation of innovation diffusion models with application to a consumer durable. Marketing Letters 6 123-136.
12. DELYON, B., LAVIELLE, M. and MOULINES, E. (1999). Convergence of a stochastic approximation version of the EM algorithm. Ann. Statist. 27 94-128.
13. DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1 977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38.
14. FORT, G., MOULINES, E., ROBERTS, G. O. and ROSENTHAL, J. S. (2003). On the geometric ergodicity of hybrid samplers. J. Appl. Probab. 40 123-146.
15. Guo, S. and THOMPSON, E. (1991). Monte-Carlo estimation of variance component models for large complex pedigrees. IMA Journal of Mathematics Applied in Medicine and Biology 8 171-189.
16. HALL, P. and HEYDE, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York.
17. JAMSHIDIAN, M. and JENNRICH, R. (1997). Acceleration of the EM algorithm by using quasi-Newton methods. J. R. Stat. Soc. Ser. B Stat. Methodol. 59 569-587.
18. MENG, X. and SCHILLING, S. (1996). Fitting full-information item factor models and an empirical investigation of bridge sampling. J. Amer. Statist. Assoc. 91 1254-1267.
19. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
20. PIERRE-LOTI-VIAUD, D. (1995). Random perturbations of recursive sequences with an application to an epidemic model. J. Appl. Probab. 32 559-578.
21. PÓLYA, G. and SZEGÖ, G. (1976). Problems and Theorems in Analysis 2. Springer, New York.
22. POLYAK, B. (1990). New stochastic approximation type procedures. Automat. Remote Control 51 937-946.
23. SHAPIRO, A. and WARDI, Y. (1996). Convergence analysis of stohastic algorithms. Math. Oper. Res. 21 615-628.1
24. SHERMAN, R., Ho, Y. and DALAL, S. (1999). Conditions for convergence of Monte Carlo EM sequences with an application to product diffusion modeling. Econom. J. 2 248-267.
25. TANNER, M. A. (1996). Tools for Statistical Inference, 3rd ed. Springer, New York.
26. WEI, G. and TANNER, M. (1990). A Monte-Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Amer. Statist. Assoc. 85 699-704.
27. Wu, C. (1983). On the convergence properties of the EM algorithm. Ann. Statist. 11 95-103.
28. ZEGER, S. L. (1988). A regression model for time series of counts. Biometrika 75 621-629.