Assessment of local influence in elliptical linear models with longitudinal structure

Computational Statistics and Data Analysis

Volumn 51, Issue 9, 2007, Pages 4354-4368

  Osorio, Felipe ^a   Paula, Gilberto A ^a   Galea, Manuel ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

Correlated data; Likelihood displacement; Matrix differential; Outliers; Regression diagnostic; Robust estimation

Indexed keywords

CORRELATION METHODS; ERROR ANALYSIS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS);

CORRELATED DATA; LIKELIHOOD DISPLACEMENT; MATRIX DIFFERENTIAL; OUTLIERS; REGRESSION DIAGNOSTIC; ROBUST ESTIMATION;

MATHEMATICAL MODELS;

EID: 34147127506     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.06.004     Document Type: Article

References (35)

1. Arellano, R., 1994. Elliptical distributions: properties, inference and applications in regression models. Unpublished Ph.D. Thesis, Department of Statistics, University of São Paulo, Brazil.
2. Beckman R.J., Nachtsheim C.J., and Cook R.D. Diagnostics for mixed-model analysis of variance. Technometrics 29 (1987) 413-426
3. Cook R.D. Assessment of local influence (with discussion). J. Roy. Statist. Soc. Ser. B 48 (1986) 133-169
4. Copt, S., Victoria-Feser, M., 2006. High breakdown inference in the mixed linear model. J. Amer. Statist. Assoc. 101, 292-300.
5. Cysneiros F.J.A., and Paula G.A. One-sided test in linear models with multivariate t-distribution. Comm. Statist. Simulation Comput. 33 (2004) 747-771
6. Dennis J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1996), SIAM Publications, Philadelphia
7. Díaz-García J.A., Galea M., and Leiva-Sánchez V. Influence diagnostics for elliptical multivariate linear regression models. Comm. Statist. Theory Methods 32 (2003) 625-641
8. Fang K.T., Kotz S., and Ng K.W. Symmetric Multivariate and Related Distributions (1990), Chapman & Hall, London
9. Fernández C., and Steel M.F.J. Multivariate Student-t regression models: pitfalls and inference. Biometrika 86 (1999) 153-167
10. Galea M., Paula G.A., and Bolfarine H. Local influence in elliptical linear regression models. The Statistician 46 (1997) 71-79
11. Galea M., Paula G.A., and Uribe-Opazo M. On influence diagnostic in univariate elliptical linear regression models. Statist. Papers 44 (2003) 23-45
12. Gómez E., Gómez-Villegas M.A., and Marín J.M. A multivariate generalization of the power exponential family of distributions. Commun. Statist. Theory Methods 27 (1998) 589-600
13. Huggins R.M. A robust approach to the analysis of repeated measures. Biometrics 49 (1993) 715-720
14. Jennrich R.I., and Schluchter M.D. Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42 (1986) 805-820
15. Kowalski J., Mendoza-Blanco J.R., Tu X.M., and Gleser L.J. On the difference in inference and prediction between the joint and independent t-error models for seemingly unrelated regressions. Commun. Statist. Theory Methods 28 (1999) 2119-2140
16. Lange K.L., Little R.J.A., and Taylor J.M.G. Robust statistical modeling using the t distribution. J Amer. Statist. Assoc. 84 (1989) 881-896
17. Lesaffre E., and Verbeke G. Local influence in linear mixed models. Biometrics 54 (1998) 570-582
18. Lindsey J.K. Multivariate elliptically contoured distributions for repeated measurements. Biometrics 55 (1999) 1277-1280
19. Little R.J.A. Robust estimation of the mean and covariance matrix from data with missing values. Appl. Statist. 37 (1988) 23-38
20. Liu S. On local influence for elliptical linear models. Statist. Papers 41 (2000) 211-224
21. Liu S. Local influence in multivariate elliptical linear regression models. Linear Algebra Appl. 354 (2002) 159-174
22. Magnus J.R., and Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics (1988), Wiley, New York
23. Nel D.G. On matrix differentiation in statistics. South African Statist. J. 14 (1980) 137-193
24. Ouwens M.J.N.M., Tan F.E.S., and Berger M.P.F. Local influence to detect influential data structures for generalized linear mixed models. Biometrics 57 (2001) 1166-1172
25. Pan J. Influential observation identification in the growth curve model with Rao's simple covariance structure. Commun. Statist. Theory Methods 31 (2002) 813-831
26. Pan J., and Bai P. Local influence analysis in the growth curve model with Rao's simple covariance structure. J. Appl. Statist. 7 (2003) 771-781
27. Pan J., Fang K.T., and von Rosen D. Local influence assessment in the growth curve model with unstructured covariance. J. Statist. Plann. Inference 62 (1997) 263-278
28. Pendergast J.F., and Broffitt J.D. Robust estimation in growth curve models. Commun. Statist. Theory Methods 14 (1985) 1919-1939
29. Pinheiro J.C., Liu C., and Wu Y.N. Efficient algorithms for robust estimation in linear mixed-effects models using the multivariate t distribution. J. Comput. Graphical Statist. 10 (2001) 249-276
30. Poon W., and Poon Y.S. Conformal normal curvature and assessment of local influence. J. Roy. Statist. Soc. Ser. B 61 (1999) 51-61
31. Potthoff R.F., and Roy S.N. A generalized multivariate analysis of a variance model useful especially for growth curve problems. Biometrika 51 (1964) 313-326
32. Savalli, C., Paula, G.A., Cysneiros, F.J.A., 2006. Assessment of variance components in elliptical linear mixed models. Statist. Model. 6, 59-76.
33. Wei B.C., Hu Y.Q., and Fung W.K. Generalized leverage and its applications. Scandinavian J. Statist. 25 (1998) 25-37
34. Welsh A.H., and Richardson A.M. Approaches to the robust estimation of mixed models. In: Maddala G.S., and Rao C.R. (Eds). Handbook of Statistics vol. 15 (1997), Elsevier Science, Amsterdam 343-384
35. Zhu H., and Lee S. Local influence for generalized linear mixed models. Canad. J. Statist. 31 (2003) 293-309