Influence analysis in skew-birnbaum-saunders regression models and applications

Journal of Applied Statistics

Volumn 38, Issue 8, 2011, Pages 1633-1649

  Santana, Lucia ^a   Vilca, Filidor ^a   Leiva, Víctor ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

EM algorithm; Extreme percentiles; Local influence; Sinh normal distribution; Skew normal distribution

Indexed keywords

EID: 78650848762     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664763.2010.515679     Document Type: Article

References (37)

1. A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171-178.
2. Azzalini, The skew-normal distribution and related multivariate families, Scand. J. Statist. 32 (2005), pp. 159-188.
3. N. Balakrishnan, V. Leiva, A. Sanhueza, and F. Vilca, Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM algorithm, Stat. Oper. Res. Trans. 33 (2009), pp. 171-192.
4. M. Barros, G.A. Paula, and V. Leiva, A new class of survival regression models with heavy-tailed errors: Robustness and diagnostics, Lifetime Data Anal. 14 (2008), pp. 316-332.
5. Z.W. Birnbaum and S.C. Saunders, A new family of life distributions, J. Appl. Probab. 6 (1969), pp. 637-652.
6. R.D. Cook, Assessment of local influence, J. R. Stat. Soc. B 48 (1986), pp. 133-169.
7. R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman and Hall, London, 1982.
8. F.J.A. Cysneiros and G.A. Paula, Restricted methods in symmetrical linear regression models, Comput. Statist. Data Anal. 49 (2005), pp. 689-708.
9. J.A. Díaz-García, M. Galea, and V. Leiva, Influence diagnostics for multivariate elliptic regression linear models, Comm. Statist. Theory Methods 32 (2003), pp. 625-641.
10. J.A. Díaz-García and V. Leiva, A new family of life distributions based on elliptically contoured distributions, J. Statist. Plann. Inference 128 (2005), pp. 445-457.
11. L.A. Escobar and W.Q. Meeker, Assessing influence in regression analysis with censored data, Biometrics 48 (1992), pp. 507-528.
12. M. Galea, V. Leiva, and G.A. Paula, Influence diagnostics in log-Birnbaum-Saunders regression models, J. Appl. Stat. 31 (2004), pp. 1049-1064.
13. M. Galea, G.A. Paula, and H. Bolfarine, Local influence in elliptical linear regression models, Statistician 46 (1997), pp. 71-79.
14. H.W. Gómez, J. Olivares, and H. Bolfarine, An extension of the generalized Birnbaum-Saunders distribution, Statist. Probab. Lett. 79 (2009), pp. 331-338.
15. N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vol. 2, John Wiley and Sons, NewYork, 1995.
16. R.E. Kass and A.E. Raftery, Bayes factors, J. Amer. Statist. Assoc. 90 (1995), pp. 773-795.
17. C.W. Kwan and W.K. Fung, Assessing local influence for specific restricted likelihood: Application to factor analysis, Psychometrika 63 (1998), pp. 35-46.
18. K.L. Lange, J.A. Little, and M.G. Taylor, Robust statistical modeling using the t distribution, J. Amer. Statist. Assoc. 84 (1989), pp. 881-896.
19. S.Y. Lee and L. Xu, Influence analyses of nonlinear mixed-effects models, Comput. Statist. Data Anal. 45 (2004), pp. 321-341.
20. V. Leiva, M. Barros, G.A. Paula, and M. Galea, Influence diagnostics in log-Birnbaum-Saunders regression models with censored data, Comput. Statist. Data Anal. 51 (2007), pp. 5694-5707.
21. V. Leiva, F. Vilca, N. Balakrishnan, and A. Sanhueza, A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443.
22. A. Lemonte and G. Cordeiro, Birnbaum-Saunders nonlinear regression models, Comput. Statist. Data Anal. 53 (2009), pp. 4441-4452.
23. A. Lucas, Robustness of the Student t based M-estimator, Comm. Statist. Theory Methods 26 (1997), pp. 1165-1182.
24. X.-L. Meng and D.B. Rubin, Maximum likelihood estimation via the ECM algorithm: A general framework, Biometrika 80 (1993), pp. 267-278.
25. E.M.M. Ortega, H. Bolfarine, and G.A. Paula, Influence diagnostics in generalized log-gamma regression models, Comput. Statist. Data Anal. 42 (2003), pp. 165-186.
26. F. Osorio, G.A. Paula, and M. Galea, Assessment of local influence in elliptical linear models with longitudinal structure, Comput. Statist. Data Anal. 51 (2007), pp. 4354-4368.
27. W.J. Owen and W.J. Padgett, Birnbaum-Saunders accelerated life model, IEEE Trans. Rel. 49 (2000), pp. 224-229.
28. G.A. Paula, Assessing local influence in restricted regression models, Comput. Statist. Data Anal. 16 (1993), pp. 63-79.
29. A.E. Raftery, Bayesian model seletion in social research, Sociol. Methods 25 (1995), pp. 111-163.
30. J.R. Rieck and J.R. Nedelman, A log-linear model for the Birnbaum-Saunders distribution, Technometrics 33 (1991), pp. 51-60.
31. A. Sanhueza, V. Leiva, and N. Balakrishnan, The generalized Birnbaum-Saunders distribution and its theory, methodology and application, Comm. Statist. Theory Methods 37 (2008), pp. 645-670.
32. D.J. Spiegelhalter, N.G. Best, B.P. Carlin, and A. van der Linde, Bayesian measures of model complexity and fit, J. R. Stat. Soc. B 64 (2002), pp. 1-34.
33. Y. Tanaka, F. Zhang, and T. Mori, Local influence in principal component analysis: Relationship between the local influence and influence function approaches revisited, Comput. Statist. Data Anal. 44 (2003), pp. 143-160.
34. E.G. Tsionas, Bayesian inference in Birnbaum-Saunders regression, Comm. Statist. Theory Methods 30 (2001), pp. 179-193.
35. F. Vilca and V. Leiva, A new fatigue life model based on family of skew-elliptical distributions, Comm. Statist. Theory Methods 35 (2006), pp. 229-244.
36. F.C. Xie and B.C. Wei, Diagnostics analysis for log-Birnbaum-Saunders regression models, Comput. Statist. Data Anal. 51 (2007), pp. 4692-4706.
37. H.T. Zhu and S.Y. Lee, Local influence for incomplete data models, J. R. Stat. Soc. B 63 (2001), pp. 111-126.