A Smooth nonparametric estimate of a mixing distribution using mixtures of gaussians

Journal of the American Statistical Association

Volumn 91, Issue 435, 1996, Pages 1141-1151

  Magder, Laurence S ^a   Zeger, Scott L ^b  

^a UNIVERSITY OF MARYLAND SCHOOL OF MEDICINE   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Deconvolution; Empirical bayes; Longitudinal data; Mixed models; Mixtures; Random effects

Indexed keywords

EID: 0030329265     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476984     Document Type: Article

References (23)

1. Bohning, D., Schlattmann, P., and Lindsay, B. (1992), "Computer-Assisted Analysis of Mixtures (C.A.MAN): Statistical Algorithms," Biometrics, 48, 283-303.
2. Breslow, N. E., and Clayton, D. G. (l993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
3. Butler, S. M., and Louis, T. A. (1992), "Random Effects Models With Non-Parametric Priors," Statistics in Medicine, 11, 1981-2000.
4. Carroll, R. J., and Hall, P. (1988), "Optimal Rates of Convergence for Deconvolving a Density," Journal of the American Statistical Association, 83, 1184--1186.
5. Davidian, M., and Gallant, A. R. (1992), “Smooth Nonparametric Maximum Likelihood Estimation for Population Pharmacokinetics, With Application to Quinidine,” Journal of Pharmacokinetics and Biopharmaceutics, 20, 529-556.
6. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
7. Follman, D. A., and Lambert, D. (1989), “Generalizing Logistic Regression by Nonparametric Mixing,” Journal of the American Statistical Association, 84, 295-300.
8. Galai, N., Muñoz, A., and Chen, K. (1993), ‘Tracking of Markers and Onset of Disease Among HIV-1 Seroconverters," Statistics in Medicine, 12, 2133-2145.
9. Gallant, A. R., and Nychka, D. W. (1987), “Semi-Nonparametric Maximum Likelihood Estimation," Econometrica, 55, 363-390.
10. Kiefer, J., and Wolfowitz, J. (1956), “Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters,” Annals of Mathematical Statistics, 27, 887-906.
11. Kaslow, R. A., Ostrow, D. G., Detels, R., Phair, J. P., Polk, B. F., Rinaldo, C. R. (1987), “The Multicentcr AIDS Cohort Study: Rationale, Organization, and Selected Characteristics of the Participants,” American Journal of Epidemiology, 126, 310-318.
12. Laird, N. M. (1978), “Nonparametric Maximum Likelihood Estimation of a Mixing Distribution,” Journal of the American Statistical Association, 73, 805-811.
13. Laird, N. M., and Louis, T. A. (1990), “Smoothing the Non-Parametric Estimate of a Prior distribution by Roughening: A Computational Study,” in Statistical Data Analysis and Inference (Supplement), ed. Y. Dodge, Amsterdam: North-Holland.
14. Lesperance, M. L., and Kalbfleisch, J. D. (1992), "An Algorithm for Computing the Nonparametric MLE of a Mixing Distribution,” Journal of the American Statistical Association, 87, 120-126.
15. Lindsay, B. G. (1983), "The Geometry of Mixture Likelihoods: A General Theory,” The Annals of Statistics, 11, 86-94.
16. Lindstrom, M. J., and Bates, D. M. (1988), “Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data,” Journal of the American Statistical Association, 83, 1014-1022.
17. Lindstrom, M. J., and Bates, D. M. (1990), “Nonlinear Mixed Effects Models for Repeated Measures Data," Biometrics, 46, 673-687.
18. Magder, L. S., “Estimating Mixing Distributions Using Mixtures of Gauss- ians,” Ph.D. dissertation, The Johns Hopkins University, Dept, of Bio- statistics.
19. Morris, C. N. (1983), “Parametric Empirical Bayes Inference: Theory and Practice,” Journal of the American Statistical Association, 78, 47-65.
20. Statistical Sciences, inc. (1992), S-Plus Version 3.1 for Sun SPARC.
21. Stefanski, L., and Carroll, R. J. (1990), “Deconvoluting Kernel Density Estimators," Statistics, 21, 169-184.
22. Zeger, S. L., and Diggle, P. J. (1994), “Semi-Parametric Models for Longitudinal Data With Application to CD4 Cell Numbers in HIV Serocon- verters,” Biometrics, 50, 689-699.
23. Zhang, C. (1990), “Fourier Methods for Estimating Mixing Densities and Distributions," The Annals of Statistics, 18, 806-831.