Robust likelihood functions in Bayesian inference

Journal of Statistical Planning and Inference

Volumn 138, Issue 5, 2008, Pages 1258-1270

  Greco, Luca ^a   Racugno, Walter ^b   Ventura, Laura ^c  

^a UNIVERSITY OF SANNIO   (Italy)

^b UNIVERSITY OF CAGLIARI   (Italy)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Estimating equation; Influence function; Kullback Leibler divergence; Model misspecification; Posterior distribution; Pseudo likelihood; Robustness

Indexed keywords

EID: 38149111130     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.05.001     Document Type: Article

References (50)

1. Adimari G. Empirical likelihood type confidence intervals under random censorship. Ann. Inst. Statist. Math. 49 (1997) 447-466
2. Adimari G., and Ventura L. Quasi-profile loglikelihood for unbiased estimating functions. Ann. Inst. Statist. Math. 54 (2002) 235-244
3. Adimari G., and Ventura L. Quasi-likelihood from M-estimators: a numerical comparison with empirical likelihood. Statist. Methods Appl. 11 (2002) 175-185
4. Andrade J.A.A., and O'Hagan A. Bayesian robustness modeling using regularly varying distributions. Bayesian Anal. 1 (2006) 169-188
5. Berger J.O. An overview of robust Bayesian analysis (with discussion). Test 3 (1994) 5-124
6. Bernardo J.M., and Smith A.F.M. Bayesian Theory (2000), Wiley Series in Probability and Statistics, New York
7. Bertolino F., and Racugno W. Analysis of the linear correlation coefficient using pseudo-likelihoods. J. Italian Statist. Soc. 1 (1992) 33-50
8. 2-test by using marginal likelihoods. Statistician 43 (1994) 191-201
9. Cabras, S., Racugno, W., Ventura, L., 2006. Bayesian inference on the scalar skew-normal distribution. In: Proceedings of COMPSTAT 2006, 17th Symposium of IASC-ERS, pp. 1373-1380.
10. David A.P. Posterior expectations for large observations. Biometrika 60 (1973) 664-667
11. Dey, D.K., Ghosh, S.H., Lou, K., 1996. On local sensitivity measures in Bayesian analysis (with discussion). In: Bayesian Robustness, IMS Lecture Notes-Monograph Series, vol. 29.
12. Efron B. Bayes and likelihood calculations from confidence intervals. Biometrika 80 (1993) 3-26
13. Gustafson P. Model influence functions based on mixtures. Canad. J. Statist. 24 (1996) 535-548
14. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., and Stahel W.A. Robust Statistics. The Approach Based on Influence Functions (1986), Wiley, New York
15. Heritier S., and Ronchetti E. Robust bounded influence tests in general parametric models. J. Amer. Statist. Assoc. 89 (1994) 897-904
16. Huber, P.J., 1967. The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. I, pp. 221-233.
17. Huber P.J. Robust Statistics (1981), Wiley, New York
18. Lavine M. Sensitivity in Bayesian statistics: the prior and the likelihood. J. Amer. Statist. Assoc. 86 (1991) 396-399
19. Lavine M. On an approximate likelihood for quantiles. Biometrika 82 (1995) 220-222
20. Lazar N.A. Bayesian empirical likelihood. Biometrika 90 (2003) 319-326
21. Markatou M., and Ronchetti E. Robust inference: the approach based on influence functions. Handbook of Statistics 15 (1997) 49-75
22. Markatou M., Basu A., and Lindsay B.G. Weighted likelihood equations with bootstrap root search. J. Amer. Statist. Assoc. 93 (1998) 740-750
23. McCullagh, P., 1991. Quasi-likelihood and estimating functions. In: Hinkley, D.V., Reid, N., Snell, E.J., (Eds.), Statistical Theory and Modelling. pp. 265-286.
24. Monahan J.F., and Boos D.D. Proper likelihoods for Bayesian analysis. Biometrika 79 (1992) 271-278
25. Monti A.C., and Ronchetti E. On the relationship between empirical likelihood and empirical saddlepoint approximation for multivariate M-estimators. Biometrika 80 (1993) 329-338
26. O'Hagan A. On outlier rejection phenomena in Bayes inference. J. Roy. Statist. Soc. B 41 (1979) 258-367
27. O'Hagan A. Modelling with heavy tails. Bayesian Statist. 3 (1988) 345-359
28. O'Hagan A. Outliers and credence for location parameter inference. J. Amer. Statist. Assoc. 85 (1990) 172-176
29. Owen A.B. Empirical Likelihood (2001), Chapman & Hall, London
30. Pace L., and Salvan A. Principles of Statistical Inference from a Neo-Fisherian Perspective (1997), World Scientific, Singapore
31. Pace L., Salvan A., and Ventura L. Likelihood based discrimination between separate scale and regression models. J. Statist. Plann. Inference 136 (2006) 3539-3553
32. Paranjpe S.A., and Gore A.P. Selecting variables for discrimination when covariance matrices are unequal. Statist. Probab. Lett. 21 (1994) 417-419
33. Passarin, K., 2004. Robust Bayesian estimation. Working Paper, 2004.11, University of Insubria, Italy.
34. Peracchi F. Robust M-estimators. Econometric Rev. 9 (1990) 1-30
35. Peracchi F. Robust M-tests. Econometric Theory 7 (1991) 69-84
36. Pericchi L.R., and Perez M.E. Posterior robustness with more than one sampling model. J. Statist. Plann. Inference 40 (1994) 279-294
37. Pericchi L.R., and Sansò B. A note on bounded influence in Bayesian analysis. Biometrika 82 (1995) 223-225
38. Racugno, W., Salvan, A., Ventura, L., 2005. On the use of pseudo-likelihoods in Bayesian variable selection. Working Paper, 2005.12, Department of Statistics, University of Padua, Italy.
39. Raftery, A.E., Madigan, D., Volinsky, C.T., 1996. Accounting for model uncertainty in survival analysis improves predictive performance. Bayesian Statist. 323-349.
40. Rios Insua D., and Ruggeri F. Robust Bayesian Analysis (2000), Springer, New York
41. Royall R. Model robust confidence intervals using maximum likelihood estimators. Internat. Statist. Rev. 54 (1986) 221-226
42. Schennach S.M. Bayesian exponentially tilted empirical likelihood. Biometrika 92 (2005) 31-46
43. Severini T.A. On the relationship between Bayesian and non-Bayesian elimination of nuisance parameters. Statist. Sinica 9 (1999) 713-724
44. Shyamalkumar N.D. Likelihood Robustness. Robust Bayesian Analysis (2000), Springer, New York
45. Sivaganesan S. Robust Bayesian diagnostic. J. Statist. Plann. Inference 35 (1993) 171-188
46. Spiegelhalter D.J. Exact Bayesian inference on the parameters of a Cauchy distribution with vague prior information. Bayesian Statist. 2 (1985) 743-750
47. Tierney L., and Kadane J.B. Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81 (1986) 82-86
48. Tsao M., and Zhou J. On the robustness of empirical likelihood ratio confidence intervals for location. Canad. J. Statist. 29 (2001) 129-140
49. Tsou T.S., and Royall R.M. Robust likelihoods. J. Amer. Statist. Assoc. 90 (1995) 316-320
50. Verdinelli I., and Wasserman L. Bayesian analysis of outlier problems using the Gibbs sampler. Statist. and Comput. 1 (1991) 105-117