Bayesian semiparametric median regression modeling

Journal of the American Statistical Association

Volumn 96, Issue 456, 2001, Pages 1458-1468

  Kottas, Athanasios ^a   Gelfand, Alan E ^b  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Censoring; Dirichlet process mixing; Linear functionals; Skewness; Split densities

Indexed keywords

EID: 1542679104     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501753382363     Document Type: Article

References (39)

1. Antoniak, C. E. (1974), “Mixtures of Dirichlet Processes With Applications to Bayesian Nonparametric Problems,” Annals of Statistics, 2, 1152-1174.
2. Brunner, L. J. (1995a), “Bayesian Linear Regression With Error Terms That Have Symmetric Unimodal Densities,” Journal of Nonparametric Statistics, 4, 335-348.
3. Brunner, L. J. (1995b), “Using the Gibbs Sampler to Simulate From the Bayes Estimate of a Decreasing Density,” Communications in Statistics A—Theory and Methods, 24, 215-226.
4. Brunner, L. J., and Lo, A. Y. (1989), “Bayes Methods for a Symmetric Unimodal Density and Its Mode,” Annals of Statistics, 17, 1550-1566.
5. Christensen, R., and Johnson, W. (1988), “Modeling Accelerated Failure Time With a Dirichlet Process,” Biometrika, 75, 693-704.
6. Dagpunar, J. (1988), Principles of Random Variate Generation, Oxford: Clarendon Press.
7. Devroye, L. (1986), Non-Uniform Random Variate Generation, New York: Springer-Verlag.
8. Doss, H. (1985a), “Bayesian Nonparametric Estimation of the Median; Part I: Computation of the Estimates,” Annals of Statistics, 13, 1432-1444.
9. Doss, H. (1985b), “Bayesian Nonparametric Estimation of the Median; Part II: Asymptotic Properties of the Estimates,” Annals of Statistics, 13, 1445-1464.
10. Escobar, M. D. (1994), “Estimating Normal Means With a Dirichlet Process Prior,” Journal of the American Statistical Association, 89, 268-277.
11. Escobar, M. D., and West, M. (1995), “Bayesian Density Estimation and Inference Using Mixtures,” Journal of the American Statistical Association, 90, 577-588.
12. Feller, W. (1971), An Introduction to Probability Theory and Its Applications (Vol. 2, 2nd ed.), New York: Wiley.
13. Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” Annals of Statistics, 1, 209-230.
14. Ferguson, T. S. (1974), “Prior Distributions on Spaces of Probability Measures,” Annals of Statistics, 2, 615-629.
15. Fernández, C., and Steel, M. F. J. (1998), “On Bayesian Modeling of Fat Tails and Skewness,” Journal of the American Statistical Association, 93, 359-371.
16. Gelfand, A. E. (1999), “Approaches for Semiparametric Bayesian Regression,” in Asymptotics, Nonparametrics and Time Series, ed. S. Ghosh, New York: Marcel Dekker, pp. 615-638.
17. Gelfand, A. E., and Kottas, A. (to appear), “A Computational Approach for Full Nonparametric Bayesian Inference under Dirichlet Process Mixture Models,” Journal of Computational and Graphical Statistics.
18. Gelfand, A. E., and Mukhopadhyay, S. (1995), “On Nonparametric Bayesian Inference for the Distribution of a Random Sample,” Canadian Journal of Statistics, 23, 411-420.
19. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398-409.
20. Geweke, J. (1989), “Bayesian Inference in Econometric Models Using Monte Carlo Integration,” Econometrica, 57, 1317-1339.
21. Groeneveld, R. A., and Meeden, G. (1984), “Measuring Skewness and Kurtosis,” Statistician, 33, 391-399.
22. Hanson, T., and Johnson, W. O. (2001), “Modeling Regression Error With a Mixture of Pólya Trees,” Technical Report, University of New Mexico, Albuquerque, NM.
23. Hettmansperger, T. P., and McKean, J. W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.
24. Johnson, W., and Christensen, R. (1989), “Nonparametric Bayesian Analysis of the Accelerated Failure Time Model,” Statistics and Probability Letters, 8, 179-184.
25. Jørgensen, B. (1982), Statistical Properties of the Generalized Inverse Gaussian Distribution, in Lecture Notes in Statistics, 9. New York: Springer-Verlag.
26. Kuo, L., and Mallick, B. (1997), “Bayesian Semiparametric Inference for the Accelerated Failure-Time Model,” Canadian Journal of Statistics, 25, 457-472.
27. Lo, A. Y. (1984), “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” Annals of Statistics, 12, 351-357.
28. MacEachern, S. N., and Müller, P. (1998), “Estimating Mixture of Dirichlet Process Models,” Journal of Computational and Graphical Statistics, 7, 223-238.
29. Powell, J. L. (1984), “Least Absolute Deviations Estimation for the Censored Regression Model,” Journal of Econometrics, 25, 303-325.
30. Richardson, S., and Green, P. J. (1997), “On Bayesian Analysis of Mixtures With an Unknown Number of Components” (with discussion), Journal of the Royal Statistical Society, Ser. B, 59, 731-792.
31. Rousseeuw, P. J., and Leroy, A. M. (1987), Robust Regression and Outlier Detection, New York: John Wiley.
32. Sethuraman, J. (1994), “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, 4, 639-650.
33. Smith, A. F. M., and Roberts, G. O. (1993), “Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods,” Journal of the Royal Statistical Society, Ser. B, 55, 3-23.
34. Tierney, L. (1994), “Markov Chains for Exploring Posterior Distributions” (with discussion), Annals of Statistics, 22, 1701-1762.
35. van Zwet, W. R. (1964), “Convex Transformations of Random Variables,” in Mathematical Centre Tracts, 7, Amsterdam: Mathematisch Centrum.
36. Walker, S. G., Damien, P., Laud, P. W., and Smith, A. F. M. (1999), “Bayesian Nonparametric Inference for Random Distributions and Related Functions” (with discussion), Journalof the Royal StatisticalSociety, Ser. B, 61, 485-527.
37. Walker, S. G., and Mallick, B. K. (1999), “A Bayesian Semiparametric Accelerated Failure Time Model,” Biometrics, 55, 477-483.
38. Yang, S. (1999), “Censored Median Regression Using Weighted Empirical Survival and Hazard Functions,” Journal of the American Statistical Association, 94, 137-145.
39. Ying, Z., Jung, S. H., and Wei, L. J. (1995), “Survival Analysis With Median Regression Models,” Journal of the American Statistical Association, 90, 178-184.