Maximization by parts in likelihood inference

Journal of the American Statistical Association

Volumn 100, Issue 472, 2005, Pages 1145-1158

  Song, Peter X K ^a   Fan, Yanqin ^b   Kalbfleisch, John D ^c   Jiang, Jiming ^d   Louis, Thomas A ^e   Liao, J G ^f   Qaqish, Bahjat F ^g   Ruppert, David ^h  

^a UNIVERSITY OF WATERLOO   (Canada)

^b VANDERBILT UNIVERSITY   (United States)

^c UNIVERSITY OF MICHIGAN   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

^f UNIVERSITY OF MEDICINE AND DENTISTRY OF NEW JERSEY   (United States)

^g IL   (United States)

^h Cornell University   (United States)

Author keywords

Copula model; Fixed point algorithm; Generalized linear mixed model; Information dominance; Iterative algorithm; Non normal random effects; Score equation; State space model

Indexed keywords

EID: 29144456020     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214505000000204     Document Type: Article

References (33)

1. Abramowitz, M., and Stegun, I. (eds.) (1964), Handbook of Mathematical Functions, Washington, DC: National Bureau of Standards.
2. Bauwens, L., and Veredas, D. (2004), "The Stochastic Conditional Duration Model: A Latent Factor Model for the Analysis of Financial Duration," Journal of Econometrics, 119, 381-412.
3. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
4. Butler, S. M., and Louis, T. A. (1992), "Random-Effects Models With Non-parametric Priors," Statistics in Medicine, 11, 1981-2000.
5. Dominitz, J., and Sherman, R. P. (2002), "Some Convergence Theory for Stochastic Iterative Procedures," unpublished manuscript, California Institute of Technology.
6. Durbin, J., and Koopman, S. J. (1997), "Monte Carlo Maximum Likelihood Estimation for Non-Gaussian State-Space Models," Biometrika, 84, 669-684.
7. Engle, R. F., and Russell, J. R. (1998), "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, 66, 1127-1162.
8. Geyer, C. J., and Thompson, E. A. (1992), "Constrained Monte Carlo Maximum Likelihood for Dependent Data," Journal of the Royal Statistical Society, Ser. B, 54, 657-699.
9. Heyde, C. C. (1997), Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation, New York: Springer-Verlag.
10. Jiang, J. (2003), "Empirical Method of Moments and Its Applications," Journal of Statistical Planning and Inference, 115, 69-84.
11. Jiang, J., and Zhang, W. (2001), "Robust Estimation in Generalized Linear Mixed Models," Biometrika, 88, 753-765.
12. Joe, H. (1997), Multivariate Models and Dependent Concepts, London: Chapman & Hall.
13. Lee, Y., and Nelder, J. A. (1996), "Hierarchical Generalized Linear Models" (with discussion), Journal of the Royal Statistical Society, Ser. B, 58, 619-678.
14. Liang, K.-Y, and Zeger, S. L. (1986), "Longitudinal Data Analysis Using Generalized Linear Models," Biometrika, 73, 13-22.
15. McCulloch, C. E., and Searle, S. R. (2001), Generalized, Linear, and Mixed Models, New York: Wiley.
16. McLeish, D. L., and Small, C. G. (1988), The Theory and Applications of Statistical Inference Functions, New York: Springer-Verlag.
17. Pinheiro, P. C., Liu, C., and Wu, Y. N. (2001), "Efficient Algorithm for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution," Journal of Computational and Graphical Statistics, 10, 249-276.
18. Song, P. X.-K. (2000), "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, 27, 305-320.
19. Verbeke, G., and Lesaffre, E. (1997), "The Effect of Misspecifying the Random Effects Distribution in Linear Mixed Models for Longitudinal Data," Computational Statistics, and Data Analysis, 23, 541-556.
20. Wakefield, J. C. (1996), "The Bayesian Approach to Population Pharmacokinetic Models," Journal of the American Statistical Association, 91, 61-76.
21. Wakefield, J. C., Smith, A. F. M., Racine-Poon, A., and Gelfand, A. E. (1994), "Bayesian Analysis of Linear and Nonlinear Population Models Using the Gibbs Sampler," Applied Statistics, 43, 201-222.
22. Zhang, D., and Davidian, M. (2001), "Linear Mixed Models With Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, 57, 795-802.
23. Clayton, D. (1996), Comment on "Hierarchical Generalized Linear Models," by Y. Lee and J. A. Nelder, Journal of the Royal Statistical Society, Ser B, 58, 657-659.
24. Jiang, J. (1999), "On Maximum Hierarchical Likelihood Estimators," Communications in Statistics, Part A - Theory and Methods, 28, 1769-1775.
25. Meilijson, I. (1989), "A Fast Improvement to the EM Algorithm on Its Own Terms," Journal of the Royal Statistical Society, Ser. B, 51, 127-138.
26. Monahan, J. (2001), Numerical Methods of Statistics, Cambridge, U.K.: Cambridge University Press.
27. Rao, C. R. (1973), Linear Statistical Inference and Its Application, New York: Wiley.
28. Robert, C. P., and Casella G. (1999), Monte Carlo Statistical Methods, New York: Springer-Verlag.
29. Wei, G., and Tanner, M. (1990), "A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms," Journal of the American Statistical Association, 85, 699-704.
30. Crainiceanu, C., Stedinger, J., Ruppert, D., and Behr, C. (2003), "Modeling the United States National Distribution of Waterborne Pathogen Concentrations With Application to Cryptosporidium Parvum" Water Resources Research, 39, 1235-1249.
31. Lehmann, E. (1999), Elements of Large-Sample Theory, New York: Springer-Verlag.
32. Ruppert, D., Wand, M., and Carroll, R. (2003), Semiparametric Regression, Cambridge, U.K.: Cambridge University Press.
33. Rai, S. N., and Matthews, D. E. (1993), "Improving the EM Algorithm," Biometrika, 49, 587-591.