Maximum trimmed likelihood estimators: A unified approach, examples, and algorithms

Computational Statistics and Data Analysis

Volumn 25, Issue 3, 1997, Pages 251-272

  Hadi, Ali S ^a   Luceño, Alberto ^b  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Least median of squares; Least squares; Least trimmed squares; Maximum likelihood; Minimum volume ellipsoid; Robust estimation

Indexed keywords

ALGORITHMS; LEAST SQUARES APPROXIMATIONS; PROBABILITY; RANDOM PROCESSES;

LEAST TRIMMED SQUARES; MAXIMUM LIKELIHOOD; MINIMUM VOLUME ELLIPSOID; ROBUST ESTIMATION;

STATISTICS;

MAXIMUM LIKELIHOOD; PROBABILITY DISTRIBUTION; TRIMMED LIKELIHOOD;

EID: 0031200989     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(97)00011-X     Document Type: Article

References (26)

1. Barnett, V., Lewis, T., 1978. Outliers in Statistical Data, Wiley, New York.
2. Bickel, P.J., Doksum, K.A., 1977. Mathematical Statistics; Basic Ideas and Selected Topics. Holden Day, San Francisco.
3. Casella, G., Berger, R. L., 1990. Statistical Inference. Wadsworth, Belmont, CA.
4. Chatterjee, S., Hadi, A.S., 1988. Sensitivity Analysis in Linear Regression. Wiley, New York.
5. Cramer, H., 1946. Mathematical Methods of Statistics. Princeton University Press, Princeton, NJ.
6. Hampel, F.R., Ronchetti, E. M., Rousseeuw, P.J., Stahel, W.A., 1986. Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
7. Hawkins, D.M., 1980. Identification of Outliers. Chapman and Hall, London.
8. Hawkins, D.M., Simonoff, J.S., 1993. High breakdown regression and multivariate estimation. Appl. Statist. 42, 423-432.
9. Huber, P.J., 1964. Robust estimation of location parameter. Ann. Math. Statist. 35, 73-101.
10. Huber, P.J., 1981. Robust Statistics. Wiley, New York.
11. Lehman, E.L., 1959. Testing Statistical Hypotheses. Wiley, New York.
12. Neykov, N., Neytchev, P., 1990. A robust alternative of the maximum likelihood estimators. COMPSTAT 1990 - Short Communications, 99-100.
13. Rao, C.R., 1973. Linear Statistical Inference and Its Applications. Wiley, New York.
14. Rohatgi, V.K., 1976. An Introduction to Probability Theory and Mathematical Statistics. Wiley, New York.
15. Rosner, B., 1977. Percentage points for the RST many outlier procedure. Technometrics 19, 307-313.
16. Rousseeuw, P.J., 1984. Least median of squares regression. J. Amer. Statist. Associ. 79, 871-880.
17. Rousseeuw, P.J., 1985. Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, G., Vincze, I., Wertz, W. (Eds.), Mathematical Statistics and Applications, Vol. B, Reidel, Dordrecht, pp. 238-297.
18. Rousseeuw, P.J., 1993. A resampling design for computing high-breakdown regression. Statist. Probab. Lett. 18, 125-128.
19. Rousseeuw, P.J., Leroy, A.M., 1987. Robust Regression and Outlier Detection. Wiley, New York.
20. Rousseeuw, P.J., van Zomeren, B.C., 1990. Unmasking multivariate outliers and leverage points (with discussion). J. Amer. Statist. Assoc. 85, 633-651.
21. Silvey, S.D., 1970. Statistical Inference. Chapman and Hall, London.
22. Simpson, D.G., Ruppert, D., Carroll, R.J., 1992. On one-step GM estimates and stability of inferences in linear regression. J. Amer. Statist. Assoc. 87, 439-450.
23. Vandev, D., Neykov, N., 1993. Robust maximum likelihood in the Gaussian case. In: Morgenthaler, S., Ronchetti, E., Stahel, W., (Eds.), New Directions in Statistical Data Analysis and Robustness, Birkhauser, Basel, pp. 259-264.
24. Xu, C.W., Shiue, W.K., 1993. Parallel algorithms for least median of squares regression. Comput. Statist. Data Anal. 16, 349-362.
25. Yohai, V.J., 1987. High breakdown-point and high efficiency robust estimates for regression. Ann. Statist. 15, 642-656.
26. Yohai, V.J., Zamar, R.H., 1988. High breakdown-point estimates of regression by means of minimization of an efficient scale. J. Amer. Statist. Assoc. 83, 406-413.