Bayesian semiparametric modelling in quantile regression

Scandinavian Journal of Statistics

Volumn 36, Issue 2, 2009, Pages 297-319

  Kottas, Athanasios ^a   KrnjajiĆ, Milovan ^b  

^a University of California Santa Cruz   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Censoring; Dependent Dirichlet processes; Dirichlet process mixture models; Median regression; Scale uniform mixtures; Skewness

Indexed keywords

EID: 67949114183     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00626.x     Document Type: Article

References (40)

1. Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to nonparametric problems. Ann, Statist. 2, 1152-1174.
2. Bernardo, J. M. & Smith, A. F. M. (2000). Bayesian theory. Wiley, Chichester.
3. Blackwell, D. & MacQueen, J. B. (1973). Ferguson distributions via Pólya urn schemes. Ann, Statist. 1, 353-355.
4. Brunner, L. J. (1992). Bayesian nonparametric methods for data from, a unimodal density. Statist. Probab. Lett., 14, 195-199.
5. Brunner, L. J. (1995). Bayesian linear regression with error terms that have symmetric unimodal densities. J. Nonparametr. Statist. 4, 335-348.
6. Brunner, L. J. & Lo, A. Y. (1989). Bayes methods for a symmetric unimodal density and its mode. Ann., Statist. 17, 1550-1566.
7. Bush, C. A. & MacEachern, S. N. (1996). A semiparametric Bayesian model for randomised block designs. Biometrika 83, 275-285.
8. De Iorio, M., Müller, P., Rosner, G. L. & MacEachern, S. N. (2004). An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99, 205-215.
9. Dunson, D. B. & Taylor, J. A. (2005). Approximate Bayesian inference for quantiles. J. Nonparametr. Statist. 17, 385-400.
10. Escobar, M. D. & West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90, 577-588.
11. Feller, W. (1971). An introduction, to probability theory and its applications, Vol. II, 2nd edn. Wiley, New York.
12. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist., 1, 209-230.
13. Gelfand, A. E. & Ghosh, S. K. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika 85, 1-11.
14. Gelfand, A. E. & Kottas, A. (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11, 289-305.
15. Gelfand, A. E. & Kottas, A. (2003). Bayesian semiparametric regression for median residual life. Scand. J. Statist. 30, 651-665.
16. Gelfand, A. E., Kottas, A. & MacEachern, S. N. (2005). Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Amer. Statist. Assoc. 100, 1021-1035.
17. Hansen, M. B. & Lauritzen, S. L. (2002). Nonparametric Bayes inference for concave distribution functions. Statist. Neerlandica 56, 110-127.
18. Hanson, T. & Johnson, W O. (2002). Modeling regression error with a mixture of Pólya trees. J. Amer. Statist. Assoc: 97, 1020-1033.
19. Hjort, N. L. & Petrone, S. (2007). Nonparametric quantile inference using Dirichlet processes. In Advances in statistical modeling and inference: essays in Honor of Kjell A, Doksum (ed. V. Nair), 463-492. World Scientific Publishing Company, Singapore.
20. Ibrahim, J. G., Chen, M.-H. & Sinha, D. (2001). Bayesian survival analysis. Springer, New York.
21. Koenker, R. (2005). Quantile regression. Cambridge University Press, New York.
22. Koenker, R. & Geling, O. (2001). Reappraising medfly longevity: a quantile regression survival analysis. J. Amer. Statist. Assoc. 96, 458-468.
23. Kottas, A. & Gelfand, A. E. (2001). Bayesian semiparametric median regression modeling. J. Amer. Statist. Assoc. 96, 1458-1468.
24. Kottas, A. & Krnjajić, M. (2005). Bayesian nonparametric modeling in quantile regression. Technical report AMS 2005-06, University of California, Santa Cruz (available at: http://www.ams.ucsc. edu/reports).
25. Kottas, A., Krnjajić, M. & Taddy, M. (2007). Model-based approaches to nonparametric Bayesian quantile regression. In Proceedings of the 2007 Joint Statistical Meetings, American Statistical Association, pp. 1137-1148.
26. Lavine, M. & Mockus, A. (1995). A nonparametric Bayes method for isotonic regression. J. Statist, Plann, Inference 46, 235-248.
27. MacEachern, S. N. (1999). Dependent nonparametric processes. In Proceedings of the 1999 Joint Statistical Meetings, American Statistical Association, pp. 50-55.
28. MacEachern, S. N. (2000). Dependent Dirichlet processes. Technical Report, Department of Statistics, The Ohio State University.
29. Müller, P., Erkanli, A. & West, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
30. Neal, R. M. (1998). Regression and classification using Gaussian process priors. In Bayesian statistics 6: Proceedings of the sixth Valencia international meeting (eds J. M. Bernardo, J. O. Berger, A. P. Dawid & A. F. M. Smith), 475-501. Oxford University Press.
31. Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9, 249-265.
32. Quintana, F. A. & Iglesias, P. L. (2003). Bayesian clustering and product partition models. J. Roy. Statist. Soc. Ser. B Statist. Methodol. 65, 557-574.
33. Royston, P. & Altman, D. G. (1994). Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion). Appl Statist. 43, 429-467.
34. Scaccia, L. & Green, P. J. (2003). Bayesian growth curves using normal mixtures with nonparametric weights. J. Comput. Graph. Statist. 12, 308-331. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4, 639-650.
35. Tsionas, E. G. (2003). Bayesian quantile inference. J. Statist. Comput. Simul. 73, 659-674.
36. Walker, S. G. & Mallick, B. K. (1999). A Bayesian semiparametric accelerated failure time model. Biometrics 55, 477-483.
37. Yang, S. (1999). Censored median regression using weighted empirical survival and hazard functions. J. Amer. Statist. Assoc. 94, 137-145.
38. Ying, Z., Jung, S. H. & Wei, L. J. (1995). Survival analysis with median regression models. J. Amer. Statist. Assoc. 90, 178-184.
39. Yu, K. & Moyeed, R. A. (2001). Bayesian quantile regression. Statist. Probab. Lett. 54, 437-447.
40. Yu, K., Lu, Z. & Stander, J. (2003). Quantile regression: applications and current research areas. The Statistician 52, 331-350.