Hypothesis testing in mixture regression models

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 66, Issue 1, 2004, Pages 3-16

  Zhu, Hong Tu ^a   Zhang, Heping ^a,b  

^a YALE UNIVERSITY   (United States)

^b YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Hypothesis testing; Logistic regression; Mixture regression; Poisson regression; Power

Indexed keywords

EID: 1042279313     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1369-7412.2003.05379.x     Document Type: Article

References (28)

1. Andrews, D. W. K. (1999) Estimation when a parameter is on a boundary: theory and applications. Econometrica, 67, 1341-1383.
2. Bickel, P. and Chernoff, H. (1993) Asymptotic distribution of the likelihood ratio statistic in a prototypical non regular problem. In Statistics and Probability: a Raghu Raj Bahadur Festschrift (eds J. K. Ghosh, S. K. Mitra, K. R. Parthasarathy and B. L. S. Prakasa Rao), pp. 83-96. New Delhi: Wiley.
3. Chen, H. and Chen, J. (2001) The likelihood ratio test for homogeneity in the finite mixture models. Can. J. Statist., 29, 201-215.
4. Chen, H., Chen, J. and Kalbfleisch, J. D. (2001) A modified likelihood ratio test for homogeneity in finite mixture models. J. R. Statist. Soc. B, 63, 19-29.
5. Chen, J. (1995) Optimal rate of convergence for finite mixture models. Ann. Statist., 23, 221-233.
6. Cheng, R. C. H. and Liu, W. B. (2001) The consistency of estimators in finite mixture models. Scand. J. Statist., 28, 603-616.
7. Cox, D. R. and Hinkley, D. V. (1974) Theoretical Statistics. London: Chapman and Hall.
8. Dachunha-Castelle, D. and Gassiat, E. (1999) Testing the order of a model using locally conic parameterization: population mixtures and stationary ARMA processes. Ann. Statist., 27, 1178-1209.
9. Diggle, P. J., Liang, K. Y. and Zeger, S. L. (2002) Analysis of Longitudinal Data, 2nd edn. New York: Oxford University Press.
10. Hansen, B. E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica, 64, 413-430.
11. Haseman, J. K. and Elston, R. C. (1972) The investigation of linkage between a quantitative trait and a marker locus. Behav. Genet., 2, 3-19.
12. Kosorok, M. R. (2003) Bootstraps of sums of independent but not identically distributed stochastic processes. J. Multlv. Anal., 84, 299-318.
13. Lemdani, M. and Pons, O. (1999) Likelihood ratio tests in contamination models. Bernoulli, 5, 705-719.
14. Lindsay, B. G. (1995) Mixture Models: Theory, Geometry and Applications. Hayward: Institute of Mathematical Statistics.
15. McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd edn. London: Chapman and Hall.
16. McLachlan, G. and Peel, D. (2000) Finite Mixture Models. New York: Wiley.
17. Pauler, D. K. and Laird, N. M. (2000) A mixture model for longitudinal data with application to assessment of noncompliance. Biometrics, 56, 464-472.
18. Pollard, D. (1990) Empirical Processes: Theory and Applications. Hayward: Institute of Mathematical Statistics.
19. Risch, N. and Zhang, H. P. (1995) Extreme discordant sib pairs for mapping quantitative trait loci in humans. Science, 268, 1584-1589.
20. Teicher, H. (1963) Identifiability of finite mixtures. Ann. Math. Statist., 34, 1265-1269.
21. Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985) The Statistical Analysis of Finite Mixture Distributions. New York: Wiley.
22. van der Vaart, A. (1996) Efficient estimation in semiparametric models. Ann. Statist., 24, 862-878.
23. Wang, P. M. and Puterman, M. L. (1998) Mixed logistic regression models. J. Agric. Biol. Environ. Statist., 3, 175-200.
24. Wang, P. M., Puterman, M. L., Cockburn, I. and Le, N. (1996) Mixed Poisson regression models with covariate dependent rates. Biometrics, 52, 381-400.
25. Zhang, H. P. and Bracken, M. (1995) Tree-based risk factor analysis of preterm delivery and small-for-gestational-age birth. Am. J. Epidem., 141, 70-78.
26. Zhang, H. P., Fui, R. and Zhu, H. T. (2003) A latent variable model of segregation analysis for ordinal outcome. J. Am. Statist. Ass., to be published.
27. Zhang, H. P. and Merikangas, K. (2000) A frailty model of segregation analysis: understanding the familial transmission of alcoholism. Biometrics, 56, 815-823.
28. Zhu, H. T. and Zhang, H. P. (2003) Hypothesis testing for finite mixture regression models (mathematical details). Technical Report. Yale University School of Medicine, New Haven.