Bayesian sensitivity analysis in elliptical linear regression models

Journal of Statistical Planning and Inference

Volumn 86, Issue 1, 2000, Pages 175-199

  Arellano Valle, R B ^a   Galea Rojas, M ^b   Zuazola, P Iglesias ^a  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

62F15; 62J05; Bayes risks; Elliptical distributions; Influence measures; J distance; L1 distance; Linear regression models

Indexed keywords

EID: 0042708496     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(99)00166-4     Document Type: Article

References (39)

1. Anderson T.W., Fang K.T. Cochran's theorem for elliptically contoured distributions. Sankhya A. 49:1987;305-315.
2. Arellano-Valle R.B., Bolfarine H. On characterizations of the. t distribution Statist. Probab. Lett. 25:1995;179-185.
3. Atkinson A.C. Regression diagnostic. Transformations and constructed variables. J. Roy. Statist. Soc. B. 44:1982;1-22.
4. Barnett, V., Lewis, T., 1994. Outliers in Statistical Data. Wiley, New York.
5. Belsley, D., Kuh, E., Welsch, R., 1980. Regression Diagnostics: Identifying Influential Data and Sources of Collinerity. Wiley, New York.
6. Box, G.E.P., Tiao, G.C., 1973. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA.
7. Cambanis S., Huang S., Simons G. On the theory of elliptical contoured distributions. J. Multivariate Anal. 11:1981;368-385.
8. Carlin B.P., Polson N.G. Inference for nonconjugate Bayesian models using the Gibbs samples. Can. J. Statist. 19:1991;399-405.
9. Chaloner K., Brant R. A Bayesian approach to outlier detection and residual analysis. Biometrika. 75:1988;651-659.
10. Chaloner, K., 1994. Residual analysis and outliers in hierarchical models. In: Freeman, P.R. et al. (Eds.), Aspects of Uncertainty: A Tribute to D.V. Lindley. Wiley, Chichester.
11. Chib S., Tiwari R.C., Jammalamadaka S.R. Bayes prediction in regressions with elliptical errors. J. Econometrics. 38:1988;349-360.
12. Chu K. Estimation and decision for linear systems with elliptical random processes. IEEE Trans. Automat. Control. 18:1973;499-505.
13. Cook D. Detection of influential observations in linear regressions. Technometrics. 19:1977;15-18.
14. Fang, K.T., Kotz, S., Ng., K.W., 1990. Symmetric Multivariate and Related Distributions. Chapman & Hall, London.
15. Geisser S. Influential observations, diagnostics and discordancy tests. J. Appl. Statist. 14:1987;133-142.
16. Geisser, S., 1991. Diagnostic, divergences and perturbation analysis. In: Stahel, W. et al. (Eds.), The IMA Volumes in Mathematics and its Applications, Vol. 34. Springer, Weisberg, pp. 89-100.
17. Gelman, A., Carlin, J., Stern, H., Rubin, D., 1997. Bayesian Data Analysis. Chapman & Hall, London.
18. Girón F.J., Martínez M., Morcillo C. A Bayesian justification for the analysis of residual and influence measures. Bayesian Statist. 4:1992;651-660.
19. Guttman I., Peña D. Outliers and influence: evaluation by Posteriori of parameters in the linear model. Bayesian Statist. 3:1988;631-640.
20. Jammalamadaka S.R., Tiwari R.C., Chib S. Bayes prediction in the linear model with spherically symmetric errors. Econom. Lett. 24:1987;39-44.
21. Justel A., Peña D. Gibbs sampling will fail in outlier problem with strong masking. J. Comput. Graph. Statist. 5(2):1996;176-189.
22. Johnson, W., Geisser, S., 1982. Assessing the predictive influence of observations. In: Kallianpur, G. et al. (Eds.), Statistics and Probability. Essay in Honor of C.R. Rao. North-Holland, Amsterdam, pp. 343-358.
23. Johnson W., Geisser S. A predictive view of the detection and characterization of influential observations in regression analysis. J. Amer. Statist. Assoc. 78:1983;137-144.
24. Johnson W., Geisser S. Estimative influence measures for the multivariate general linear model. J. Statist. Plann. Inference. 11:1985;33-56.
25. Kano Y. Consistency property of elliptical probability density functions. J. Multivariate Anal. 51:1994;139-147.
26. Kelker D. Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhya A. 32:1970;419-430.
27. Kempthorne P.J. Decision-theoretic measures of influence in regression. J. Roy. Statist. Soc. B. 48:1986;370-378.
28. Meinhold R.J., Singpurwalla N.D. Robustification of kalman filter models. J. Amer. Statist. Assoc. 84:1989;479-486.
29. Osiewalski J., Steel M. Robust Bayesian inference in elliptical regression models. J. Econometrics. 57:1993;345-363.
30. Osiewalski, J., Steel, M., 1996. Posterior moments of scale parameters in elliptical regression models. In: Berry, D. et al. (Eds.), Bayesian Analysis in Statistics and Econometrics. Essays in Honor of Arnold Zellner. Wiley, New York, pp. 323-335.
31. Peng F., Dey D.K. Bayesian analysis of outlier problems using divergences measures. Can. J. Statist. 23:1995;199-213.
32. Pettit L.I. Bayes factors for outlier models using the device of imaginary observations. J. Amer. Statist. Assoc. 87:1992;541-545.
33. Pettit L.I. Bayes method for outliers in exponential samples. J. Roy. Statist. Soc. B. 50:1988;371-380.
34. Pettit L.I., Smith A.F.M. Outlier and influential observations in linear models. Bayesian Statist. 2:1985;473-494.
35. Weiss R., Cook D. A graphical case statistic for assessing posterior influence. Biometrika. 79:1992;51-55.
36. Weiss R. Influence diagnostic with the Gibbs sampler. Comput. Sci. Statist. 24:1992;266-270.
37. Weiss R. An approach to Bayesian sensitivity analysis. J. Roy. Statist. Soc. B. 58:1996;739-750.
38. West M. Outlier models and prior distribution in Bayesian linear regression. J. Roy. Statist. Soc. B. 46:1984;431-439.
39. Zellner A. Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms. J. Amer. Statist. Assoc. 71:1976;400-405.