Robust location and scale estimation based on the univariate generalized t(GT) distribution

Communications in Statistics - Theory and Methods

Volumn 32, Issue 8, 2003, Pages 1505-1525

  Arslan, Olcay ^a   Genç, Ali I ^a  

^a CUKUROVA UNIVERSITY   (Turkey)

Author keywords

Box and Tiao (BT) distribution; Generalized gamma (GG) distribution; Influence function; M estimation; Maximum likelihood estimation; Robustness; Univariate GT distribution

Indexed keywords

MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); THEOREM PROVING;

BOX AND TIAO DISTRIBUTION; GENERALIZED GAMMA DISTRIBUTION; INFLUENCE FUNCTION; M-ESTIMATION; SCALE ESTIMATION; UNIVARIATE GT DISTRIBUTION;

PROBABILITY DISTRIBUTIONS;

EID: 0043207313     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120022242     Document Type: Article

References (23)

1. Arslan O. (1992). Multivariate Robust Analysis Based on the T Distribution and the EM Algorithm. Unpublished Ph.D. Thesis, Leeds University, Leeds, UK.
2. Arslan, O. (2003). A simple test to identify good solutions of redescending M estimating equations for regression. In: Dutter, R., Filzmoser, P., Gather, U., Rousseeuw, P. J., eds. Developments in Robust Statistics, Proceedings of ICORS 2001. Physica-Verlag, pp. 50-61.
3. Bollershev, T., Engle, R. F., Nelson, D. B. (1994). ARCH models. In: Engle, R. F., McFadden, D. L., eds. Handbook of Econometrics, 4. Elsevier Science, pp. 2959-3038.
4. Box, G. E. P., Tiao, G. C. (1962). A further look at robustness via Bayes Theorem. Biometrika 49:419-432.
5. Butler, R. J., McDonald, J. B., Nelson, R. D., White, S. B. (1990). Robust and partially adaptive estimation of regression models. The Review of Economics and Statistics 72:321-327.
6. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., Stahel, W. A. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: John Wiley.
7. Hardy, G. H., Littlewood, J. E., Pólya, G. (1997). Inequalities, 2nd ed. Cambridge University Press.
8. Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions. Vol. 2, 2nd ed. New York: John Wiley.
9. Lange, K. L., Little, J. A., Taylor, J. M. G. (1989). Robust statistical modeling using the t distribution. Journal of the American Statistical Association 84:881-896.
10. Lucas, A. (1997). Robustness of the Student t based M-estimator. Commun. Statist.-Theory Meth. 26(5):1165-1182.
11. Lye, J. N., Martin, V. L. (1993). Robust estimation, nonnormalities and generalized exponential distributions. Journal of the American Statistical Association 88:261-267.
12. Mäkeläinen, T., Schmidt, K., Styan, G. P. H. (1981). On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples. Annals of Statistics 9:758-767.
13. McDonald, J. B. (1989). Partially adaptive estimation of ARMA time series models. International Journal of Forecasting 5:217-230.
14. McDonald, J. B., Butler, R. J. (1987). Some generalized mixture distributions with an application to unemployment duration. The Review of Economics and Statistics 69:232-240.
15. McDonald, J. B., Nelson, R. D. (1989). Alternative beta estimation for the market model using partially adaptive techniques. Commun. Statist.-Theory Meth. 18(11):4039-4058.
16. McDonald, J. B., Nelson, R. D. (1993). Beta estimation in the market model: skewness and leptokurtosis. Commun. Statist.-Theory Meth. 22(10):2843-2862.
17. McDonald, J. B., Newey, W. K. (1988). Partially adaptive estimation of regression models via the generalized t distribution. Econometric Theory 4:428-457.
18. Morgenthaler, S. (1990). Fitting redescending M-estimators in regression. In: Lawrence, K. D., Arthur, J. L., eds. Robust Regression: Analysis and Applications. New York: Marcel Dekker, Inc., pp. 105-128.
19. Oliver, E. H. (1972). A maximum likelihood oddity. The American Statistician 26(3):43-44.
20. Petruccelli, J. D., Nandram, B., Chen, M. (1999). Applied Statistics for Engineers and Scientists. Prentice Hall.
21. Rohatgi, V. K. (1976). An Introduction to Probability Theory and Mathematical Statistics. New York: John Wiley.
22. Theodossiou, P. (1998). Financial data and the skewed generalized t distribution. Management Science Part 1 12:1650-1661.
23. Yuh, L., Hogg, R. V. (1988). On adaptive M-regression. Biometrics 44:433-445.