Pointwise and functional approximations in Monte Carlo maximum likelihood estimation

Statistics and Computing

Volumn 9, Issue 2, 1999, Pages 91-99

  Kuk, Anthony Y C ^a   Cheng, Yuk W ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

EM algorithm; Gibbs sampling; Hierarchical likelihood; Importance sampling; Marginal likelihood; Newton Raphson procedure; Random effects

Indexed keywords

EID: 0009906557     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008800715000     Document Type: Article

References (23)

1. Anderson, D. A. and Aitkin, M. A. (1985) Variance component models with binary response: interviewer variability. J. R. Statist. Soc. B, 47, 203-210.
2. Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models. J. Am. Statist. Ass., 88, 9-25.
3. Chan, K. S. and Ledolter, J. (1995) Monte Carlo EM estimation for time series models involving counts. J. Amer. Statist. Assoc., 90, 242-252.
4. 2)dt: application to logistic-normal models. J. Am. Statist. Ass., 85, 464-469.
5. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B, 39, 1-38.
6. Geyer, C. J. (1994) On the convergence of Monte Carlo maximum likelihood calculations. J. R. Statist. Soc. B., 56, 261-274.
7. Geyer, C. J. and Thompson, E. A. (1992) Constrained maximum likelihood for dependent data (with discussion). J. R. Statist. Soc. B., 54, 657-699.
8. Karim, M. R. and Zeger, S. L. (1992) Generalized linear models with random effects; salamander mating revisited. Biometrics, 48, 631-644.
9. Kleinman, J. C. (1973) Proportions with extraneous variance: single and independent samples. J. Amer. Statist. Assoc., 68, 46-54.
10. Kuk, A. Y. C. and Cheng, Y. W. (1997) The Monte Carlo Newton-Raphson algorithm. J. Statist. Comput. Simul., 59, 233-250.
11. Lange, K. (1995) A gradient algorithm locally equivalent to the EM algorithm. J. R. Statist. Soc. B, 57, 425-437.
12. Lee, Y. and Nelder, J. A. (1996) Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B, 58, 619-678.
13. Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. J. R. Statist. Soc. B, 44, 226-233.
14. McCulloch, C. E. (1997) Maximum likelihood algorithms for generalized linear mixed models. J. Am. Statist. Assoc., 92, 162-170.
15. McGilchrist, C. A. (1994) Estimation in generalized mixed models. J. R. Statist. Soc. B, 56, 61-69.
16. McGilchrist, C. A. and Aisbett, C. W. (1991a) Restricted BLUP for mixed linear models. Biometr. J., 32, 545-550.
17. McGilchrist, C. A. and Aisbett, C. W. (1991b) Regression with frailty in survival analysis. Biometrics, 47, 461-466.
18. Penttinen, A. (1984) Modelling interaction in spatial point patterns: parameter estimation by the maximum likelihood method. Jy. Stud. Comput. Sci. Econ. Statist., 7, 1-105
19. Schall, R. (1991) Estimation in generalised linear models with random effects. Biometrika, 78, 719-727.
20. Smith, D. M. (1983) Maximum likelihood estimation of the parameters of the beta binomial distribution. Applied Statist., 32, 196-204.
21. Wei, G. C. G. and 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.
22. Weil, C. S. (1970) Selection of the valid number of sampling units and consideration of their combination in toxicological studies involving reproduction, teratogenesis or carcinogenesis. Food and Cosmetic Toxicology, 8, 177-182.
23. Zeger, S. L. (1988) A regression model for time series of counts. Biometrika, 75, 621-629.