Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Statistics

Volumn 44, Issue 6, 2010, Pages 541-556

  Lachos, V H ^a   Labra, F V ^a   Bolfarine, H ^b   Ghosh, Pulak ^c  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c INDIAN INSTITUTE OF MANAGEMENT BANGALORE   (India)

Author keywords

Em algorithm; Mahalanobis distance; Measurement error models; Scale mixtures of the skew normal distribution

Indexed keywords

EID: 78649709032     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880903236926     Document Type: Article

References (30)

1. C.L. Cheng and J.W. Van Ness, Statistical Regression with Measurement Error, Arnold, London, 1999.
2. V.D. Barnett, Simultaneous pairwise linear structural relationships, Biometrics 25 (1969), pp. 129-142.
3. H. Bolfarine and M. Galea-Rojas, On structural comparative calibration under a t-model, Comput. Stat. 11 (1996), pp. 63-85.
4. E. Chipkevitch, R. Nishimura, D. Tu, and M. Galea-Rojas, Clinical measurement of testicular volume in adolescents: comparison of the reliability of 5 methods, J. Urol. 156 (1996), pp. 2050-2053.
5. G. Kelly, The influence function in the errors in variables problem, Ann. Statist. 12 (1984), pp. 87-100.
6. G. Dunn, Design and Analysis of Reliability: The statistical Evaluation of Measurement Errors, Edward Arnold, NewYork, 1992.
7. M. Galea-Rojas, H. Bolfarine, and F.V. Labra, Local influence in comparative calibration models under elliptical t-distribution, Biom. J. 47 (2005), pp. 691-706.
8. R.B. Arellano-Valle, S. Ozan, H. Bolfarine, and V.H. Lachos, Skew normal measurement error models, J. Multivar. Anal. 98 (2005), pp. 265-281.
9. M. Branco and D. Dey, A general class of multivariate skew-elliptical distribution, J. Multivar. Anal. 79 (2001), pp. 93-113.
10. D.F. Andrews and C.L. Mallows, Scale mixtures of normal distributions, J. Roy. Statist. Soc. B, 36 (1974), pp. 99-102.
11. R.B. Arellano-Valle, M.D. Branco, and M.G. Genton, A unified view on skewed distributions arising from selections, Can. J. Stat. 34 (2006), pp. 581-601.
12. A. Azzalini and A. Dalla-Valle, The multivariate skew-normal distribution, Biometrika 83 (1996), pp. 715-726.
13. A. Azzalini and A. Capitanio, Statistical applications of the multivariate skew-normal distributions, J. Roy. Statist. Soc. B, 61 (1999), pp. 579-602.
14. V.H. Lachos, P. Ghosh, and R.B. Arellano-Valle, Likelihood based inference for skew-normal/independent linear mixed models, Statist. Sinica (in press 20, (2010)).
15. K.L. Lange, and J. S. Sinsheimer, Normal/independent distributions and their applications in robust regression, J. Comput. Graph. Stat. 2 (1993), pp. 175-198.
16. A. Azzalini and M.G. Genton, Robust likelihood methods based on the skew-t and related distributions, Int. Statist. Rev. 76 (2008), pp. 106-129.
17. J. Wang and M. Genton, The multivariate skew-slash distribution, J. Statist. Plann. Inference 136 (2006), pp. 209-220.
18. H. Bolfarine and M. Galea-Rojas, Maximum likelihood estimation of simultaneous pairwise linear structural ralationships, Biom. J. 37 (1995), pp. 673-689.
19. A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. B, 39 (1977), pp. 1-22.
20. X.L. Meng, and D.B. Rubin, Maximum likelihood estimation via the ECM algorithm: a general framework, Biometrika 80 (1993), pp. 267-278.
21. R.B. Arellano-Valle, H. Bolfarine, and V.H. Lachos, Skew-normal linear mixed models, J. Data Sci. 3 (2005), pp. 415-438.
22. K.L. Lange, J.A. Little, and M.G.J. Taylor, Robust statistical modeling using the t distribution, J. Amer. Statist. Assoc. 84 (1989), pp. 881-896.
23. A. Lucas, Robustness of the Student t based M estimator, Commun. Stat. Theory Methods 26 (1997), pp. 165-1182.
24. T.I. Lin, and J.C. Lee, Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data, Stat. Med. 27 (2008), pp. 1490-1507.
25. N. Loperfido, Modeling maxima of longitudinal contralateral observations, Test 17 (2008), pp. 370-380.
26. M. Galea-Rojas, H. Bolfarine, and M. de Castro, Local influence in comparative calibration models, Biom. J. 44 (2002), pp. 59-81.
27. Q. Vuong, Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica, 57 (1989), pp. 307-333.
28. A.E. Raftery, Bayesian model selection in social research (with discussion), Sociol. Methodol. 25 (1995), pp. 111-196.
29. X.L. Meng, and D. Van Dyk, The EM algorithm: an old folk-song sung to a fast new tune (with discussion), J. Roy. Statist. Soc. B, 59 (1997), pp. 511-567.
30. C.H. Liu, D.B. Rubin, and Y. Wu, Parameter expansion to accelerate EM: the PX-EM algorithm, Biometrika, 85 (1998), pp. 755-770.