Influential observations in the functional measurement error model

Journal of Applied Statistics

Volumn 34, Issue 10, 2007, Pages 1165-1183

  Vidal, Ignacio ^a   Iglesias, Pilar ^b   Galea, Manuel ^c  

^a UNIVERSIDAD DE TALCA   (Chile)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^c UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

Bayes risk; Gibbs sampling; Influence measures; MEM; Metropolis Hastings; Perturbation function; q divergence

Indexed keywords

EID: 36849004508     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664760701592703     Document Type: Article

References (39)

1. Abdullah, M. B. (1995) Detection of influential observations in functional errors-in-variables model. Commun-ications in Statistics: Theory and Methods, 24:6, pp. 1585-1595.
2. Aoki, R., Achcar, J. A., Bolfarine, H. and Singer, J. M. (2003) Bayesian analysis of null intercept errors-in-variables regression for pretest/ post-test data. Journal of Applied Statistics, 30, pp. 3-12.
3. Arellano-Valle, R. B., Galea-Rojas, M. and Iglesias, P. (2000) Bayesian sensitivity analysis in elliptical linear regression models. Journal of Statistical Planning and Inference, 86, pp. 175-199.
4. Berger, J. O. (1985) Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York
5. Bernardo, J. M. and Smith, A. F. M. (1994) Bayesian Theory, Wiley, Chichester
6. Best, N. G., Cowles, M. K. and Vines, S. K. (1997) CODA: Convergence Diagnosis and Output Analysis Software for Gibbs sampling output: Version 0.4, MRC Biostatistics Unit, Cambridge
7. Carrol, R. J., Ruppert, D. and Stefanski, L. A. (1995) Measurement Error in Nonlinear Models, Chapman & Hall, London
8. Chatterjee, S. and Hadi, A. S. (1988) Sensivity Analysis in Linear Regression, Wiley, New York
9. Chen, M. H., Shao, Q. M. and Ibrahim, J. G. (2000) Monte Carlo Methods in Bayesian Computation, Springer-Verlag, New York
10. Cheng, C. -L. and van Ness, J. W. (1999) Statistical Regression with Measurement Error, 6, Arnold, London
11. Cook, R. D. (1977) Detection of influential observations in linear regression. Technometrics, 19, pp. 15-18.
12. Cook, R. D. (1987) Influence assessment. Journal of Applied Statistics, 14, pp. 117-131.
13. Cook, R. D. and Weisberg, S. (1982) Residuals and Influence in Regression, Chapman & Hall, London
14. Csiszár, I. (1967) Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar., 2, pp. 299-318.
15. Dellaportas, P. and Stephens, D. A. (1995) Bayesian analysis of errors in variable regression models. Biometrics, 51, pp. 1085-1095.
16. Florens, J. P., Mouchart, M. and Richard, J. F. (1974) Bayesian inference in error-in-variables models. Journal of Multivariate Analysis, 4, pp. 419-452.
17. Fuller, W. A. (1987) Measurement Error Models, Wiley, New York
18. Galea, M., Bolfarine, H. and Vilca-Labra, F. (2002) Influence diagnostics for the structural errors-in-variables model under the student-t distribution. Journal of Applied Statitics, 29:8, pp. 1191-1204.
19. Galea, M., Bolfarine, H. and de Castro, M. (2002) Local influence in comparative calibration models. Biometrical Journal, 41, pp. 59-81.
20. Girón, F. J., Martínez, M. and Morcillo, C. (1992) A Bayesian justification for the analysis of residual and influence measures. Bayesian Statistics, 4, pp. 651-660. Oxford University Press, Oxford
21. Guttman, I. and Peña, D. (1988) Outliers and influence: Evaluation by posteriors of parameters in the linear model. Bayesian Statistics, 3, pp. 631-640. Oxford University Press, Oxford
22. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their Applications. Biometrika, 57, pp. 97-109.
23. Kass, R. E., Tierney, L. and Kadane, J. B. (1989) Approximate methods for assessing influence and sensitivity in Bayesian analysis. Biometrika, 76, pp. 663-674.
24. Kelly, G. E. (1984) The influence function in the errors in variables problem. The Annals of Statistics, 12, pp. 87-100.
25. Kempthorne, P. J. (1986) Decision-theoretic measures of influence in regression. Journal of the Royal Statistical Society B, 48, pp. 370-378.
26. Kim, M. G. (2000) Outliers and influential observations in the structural errors-in-variables model. Journal of Applied Statistics, 27:4, pp. 451-460.
27. Lee, A. H. and Zhao, Y. (1996) Assessing local influence in measurement error models. Biometrical Journal, 38, pp. 829-841.
28. Lindley, D. V. and El-Sayyad, G. M. (1968) The Bayesian estimation of a linear functional relationship, Journal of Royal Statistical Society B.30, pp. 190-202.
29. Muller, P. and Roeder, K. (1997) A Bayesian semiparametric model for case-control studies with errors in variables. Biometrika, 84, pp. 523-537.
30. O'Hagan, A. (1994) Bayesian Inference. Kendall's Advanced Theory of Statistics, 2, Edward Arnold, London
31. Peng, F. and Dey, D. K. (1995) Bayesian analysis of outlier problems using divergences measures. The Canadian Journal of Statistics, 23, pp. 199-213.
32. Richardson, S. (1996) Measurement error. Markov Chain Monte Carlo in Practice, pp. 401-414. Chapman & Hall, London
33. Robert, C. P. and Casella, G. (1999) Monte Carlo Statistical Methods, Springer-Verlag, New York
34. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society B, 55, pp. 3-23.
35. Villegas, C. (1972) Bayesian inference in linear relations. Ann. Math. Statis., 43, pp. 1767-1791.
36. Weiss, R. E. (1996) An approach to Bayesian sensitivity analysis. Journal of the Royal Statistical Society B, 58, pp. 739-750.
37. Weiss, R. E. and Cook, R. D. (1992) A grafical case statistic for assessing posterior influence. Biometrika, 79, pp. 51-55.
38. Wellman, M. J. and Gunst, R. F. (1991) Influence diagnostics for linear measurement error models. Biometrika, 78:2, pp. 373-380.
39. Zellner, A. (1971) An Introduction to Bayesian Inference in Econometrics, Wiley, New York