Bayesian local influence for the growth curve model with Rao's simple covariance structure

Journal of Multivariate Analysis

Volumn 58, Issue 1, 1996, Pages 55-81

  Pan, Jian Xin ^a,b   Fang, Kai Tai ^a,c   Liski, Erkki P ^d  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b YUNNAN UNIVERSITY   (China)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^d TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Bayesian hessian matrix; Bayesian local influence; Covariance weighted perturbation; Growth curve model; Kullback Leibler divergence; Statistical diagnostics

Indexed keywords

EID: 0030187399     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0039     Document Type: Article

References (34)

1. COOK, R. D. (1986). Assessment of local influence (with discussion). J. Roy. Statist. Soc. Ser. B 48 133-169.
2. FANG, K. T., AND XU, J. L. (1990). The direct operations of symmetric and lower-triangular matrices with their applications, in "Statistical Inference in Elliptically Contoured and Related Distributions," (K. T. Fang and T. W. Anderson, Eds.), pp. 441-455. Allerton, New York.
3. FANG, K. T., AND ZHANG, Y. T. (1990), "Generalized Multivariate Analysis," Springer-Verlag/Science Press, Berlin/Beijing.
4. GEISSER, S. (1970). Bayesian analysis of growth curves. Sankhya Ser. A 32 53-64.
5. GEISSER, S. (1985). On the prediction of observables: A selective update. In "Bayesian Statistics," Vol. 2 (J. M. Bernardo, et al., Eds.), pp. 203-230. North-Holland/Elsevier, Amsterdam.
6. GUTTMAN, I., AND PEÑA, D. (1993). A Bayesian look at diagnostics in the univariate line model, Statistica Sinica 3 367-390.
7. KARIYA, T. (1985). "Testing in the Multivariate General Linear Model," Kinokuniya Comp., Tokyo.
8. KHATRI, C. G. (1966). A note on a MANOVA model applied to problems in growth curve, Ann. Inst. Statist. Math. 18 75-86.
9. LAVINE, M. (1992). Local predictive influence in Bayesian linear models with conjugate priors. Comm. Statist. Simulation Compt. 21 269-283.
10. LEE, J. C. (1988). Prediction and estimation of growth curve with special covariance structure. J. Amer. Statist. Assoc. 83 432-440.
11. LEE, J. C. (1991). Tests and model selection for the general growth curve model. Biometrics 47 147-159.
12. LEE, J. C., AND GEISSER, S. (1972). Growth curve prediction. Sankhya Ser A 34 393-412.
13. LISKI, E. P. (1991). Detecting influential measurements in a growth curve model. Biometrics 47 659-668.
14. MACULLOCH, N. E. (1989). Local model influence. J. Amer. Statist. Assoc. 84 473-478.
15. NEL, D. G. (1980). On matrix differentiation in statistics, South African Statist. J. 14 137-193.
16. OKAMATO, M. (1973). Distinctness of the eigenvalues of a quadratic form in a multivariate sample. Ann. Statist. 1 763-765.
17. PAN, J. X. (1988). Generalized least square estimator of regression parameters and Gauss-Markov theorem in growth curve model. J. Math. Statist. Appl. Probab. 3, No. 2 169-185.
18. PAN, J. X. (1995). "Multivariate Statistical Diagnostics with Application to the Growth Curve Model." Unpublished Ph.D. dissertation. Dept. of Math., Hong Kong Baptist University.
19. PAN, J. X., AND FANG, K. T. (1995a). Multiple outlier detection in growth curve model with unstructured covariance matrix. Ann. Inst. Statist. Math. 47, No. 1 137-153.
20. PAN, J. X., AND FANG, K. T. (1995b). Detecting influential observations in growth curve model with unstructured covariance. Comput. Statist. Data Anal., in press.
21. PAN, J. X., FANG, K.T., AND VON ROSEN, D. (1995). Local influence assessment in the growth curve model with unstructured covariance. J. Statist. Plann. Inference, in press.
22. POTTHOFF, R. F., AND ROY, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 51 313-326.
23. RAO, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika 52 447-458.
24. RAO, C. R. (1966). Covariance adjustment and related problems in multivariate analysis. In "Multivariate Analysis," (P. Krishnaiah, Ed.), pp 87-103. Academic Press, New York.
25. RAO, C. R. (1967). Least square theory using an estimated dispersion matrix and its applications to measurement of signals. In "Proc. 5th Berkeley Symposium," Vol. 1, pp. 355-372.
26. RAO, C. R. (1984). Prediction of future observations in polynomial growth curve models. In "Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions," pp. 512-520. Indian Statistical Institute, Calcutta.
27. RAO, C. R. (1987). Prediction of future observations in growth curve models. Statist. Sci. 2 434-471.
28. SHIH, J, AND WEI, B. (1995). Bayesian local influence. Math. Appl. 8 237-245.
29. SWAMY, P. A. V. B. (1971). Statistical inference in random coefficient regression models, in "Lecture Notes in Operational Research and Mathematical Systems," Vol. 55. Springer-Verlag, New York.
30. VON ROSEN, D. (1988). Moments for matrix normal variables. Statistics 19 575-583.
31. VON ROSEN, D. (1989). Maximum likelihood estimates in multivariate linear normal model. J. Multivariate Anal. 31 187-200.
32. VON ROSEN, D. (1990). Moments for a multivariate linear normal model with application to growth curve model. J. Multivariate Anal. 35 243-259.
33. VON ROSEN, D. (1991). The Growth Curve Model: A Review. Comm. Statist. Theory Methods. 20(9) 2791-2822.
34. VON ROSEN, D. (1995). Influential observations in multivariate linear models. Scand. J. Statist. 22, 207-222.