Some results for robust GM-based estimators in heteroscedastic regression models

Journal of Statistical Planning and Inference

Volumn 89, Issue 1-2, 2000, Pages 215-242

  Bianco, Ana ^a   Boente, Graciela ^b   Di Rienzo, Julio ^c  

^a INSTITUTO DE CÁLCULO   (Argentina)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^c UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

Author keywords

Asymptotic properties; Heteroscedasticity; High breakdown point estimates; Primary 62F35; Robust estimation; Secondary 62J05

Indexed keywords

EID: 0010981994     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(00)00093-8     Document Type: Article

References (31)

1. Bickel P. Using residuals robustly I. Test for heteroscedasticity, nonlinearity. Ann. Statist. 6:1978;266-291.
2. Bickel P., Wichura M. Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42:1971;1656-1670.
3. Box G., Hill W. Correcting inhomogeinity of variance with power transformation weighting. Technometrics. 16:1974;385-389.
4. Carroll R.J. Adapting for heteroscedasticity in linear models. Ann. Statist. 10:1982;1224-1233.
5. Carroll R.J., Ruppert D. Robust estimation in heteroscedastic linear models. Ann. Statist. 10:1982;429-441.
6. Carroll R.J., Ruppert D. Transformations and Weighting in Regression. 1988;Chapman & Hall, London.
7. Croux C. Efficient high-breakdown M-estimators of scale. Statist. Probab. Lett. 19:1994;371-379.
8. Davidian M., Carroll R.J. Variance function estimation. J. Amer. Statist. 82:1987;1079-1091.
9. Dixon S.L., McKean J.W. Rank-based analysis of the heteroscedastic linear model. J. Amer. Statist. 91:1996;699-712.
10. Donoho D., Huber P. The notion of breakdown point. Lehmann L., Bickel P.J., Doksum K.A., Hodges J.L. A Fetschift for Erich. 1983;157-184 Wadsworth, Belmont, CA.
11. Fraiman, R., Meloche, J., 1996. Multivariate L-estimates, unpublished manuscript.
12. Gale D., Nikaidô H. The Jacobian matrix and global univalence of mappings. Math. Annalen. 159:1965;81-93.
13. Giltinan D.M., Carroll R.J., Ruppert D. Some new estimation methods for weighted regression when there are possible outliers. Technometrics. 28:1986;219-230.
14. Hampel F. A general qualitative definition of robustness. Ann. Math. Statist. 42:1971;1887-1896.
15. He X., Portnoy S. Reweighted LS estimators converge at the same rate as the initial estimator. Ann. Statist. 20:1992;2161-2167.
16. Jobson J., Fuller W. Least square estimation when the covariance matrix and the parameter vector are functionally related. J. Amer. Statist. Assoc. 75:1980;176-181.
17. Kent J., Tyler D. Redescending M-estimates of multivariate location and scatter. Ann. Statist. 19:1991;2102-2119.
18. Koul, H.L., 1992. Weighted Empiricals and Linear Models, Lecture Notes-Monograph Series, Vol. 21. Institute of Mathematical Statistics.
19. Maronna R. Robust M-estimates of multivariate location and scatter. Ann. Statist. 4:1976;51-57.
20. Maronna R., Bustos O., Yohai V. Bias and efficiency-robustness of general M-estimators for regression with random carriers. Gasser T., Rosenblatt H. Smoothing Techniques for Curve Estimation. 1979;Springer, New York.
21. Maronna R., Stahel W., Yohai V. Bias-robust estimators of multivariate scatter based on projections. J. Multivariate Anal. 42:1992;141-161.
22. Maronna R., Yohai V. Asymptotic behavior of General M-estimates for regression and scale with random carriers. Z. Wahrscheinlichkeitstheoric Verw. Geb. 58:1981;7-20.
23. Maronna R., Yohai V. Recent results on bias-robust regression estimates. Stahel W., Weisberg S. Directions in Robust Statistics and Diagnostics, Part I. 1991;221-232 Springer, New York.
24. Müller H., Stadtmüller U. Estimation of heteroscedasticity in regression analysis. Ann. Statist. 15:1987;610-625.
25. Nanayakhara N., Cressie N. Robustness to unequal scale and other departures from the classical linear model. Stahel W., Weisberg S. Directions in Robust Statistics and Diagnostics, Part II. 1991;65-113 Springer, New York.
26. Rousseeuw P.J. Least median of squares regression. J. Amer. Statist. Assoc. 79:1984;871-880.
27. Rousseeuw P., van Zomeren B. Unmasking multivariate outliers and leverage points. J. Amer. Statist. Assoc. 85:1990;633-639.
28. Rousseeuw, P., Yohai, V. 1984. Robust regression by means of S-estimates. In: Franke, J., Härdle, W., Martin, R. (Eds.), Robust and Nonlinear Time Series. Lecture Notes in Statistics, Vol. 26. Springer, New York, pp. 256-272.
29. Simpson D., Ruppert D., Carroll R.J. On one-step GM-estimates and stability of inferences in linear regressions. J. Amer. Statist. Assoc. 87:1992;439-450.
30. Welsh A., Carroll R.J., Ruppert D. Fitting heteroscedastic regression models. J. Amer. Statist. Assoc. 89:1994;100-116.
31. Yohai V., Zamar R. High breakdown estimates of regression by means of the minimization of an efficient scale. J. Amer. Statist. Assoc. 83:1988;406-413.