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Abstract:

In this paper, we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations. These estimators are robust against high-leverage outliers and they generalize the LMS (least median of squares), S. MM and τ-estimators for linear regression. An important contribution of this paper is that we can define consistent estimators using a bounded loss function (or equivalently, a re-descending score function). Since the calculation of these estimators can be computationally costly, we propose an efficient algorithm to compute them. We illustrate their use on an example and present simulation studies that show that these estimators also have good finite sample properties. © Institute of Mathematical Statistics, 2008.

Registro:

Documento: Artículo
Título:High breakdown point robust regression with censored data
Autor:Salibian-Barrera, M.; Yohai, V.J.
Filiación:University of British Columbia
Universidad de Buenos Aires
Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Departamento de Matemática, Universidad de Buenos Aires, 1426 Buenos Aires, Argentina
Palabras clave:Accelerated failure time models; Censored data; High breakdown point estimates; Linear regression model; Robust estimates
Año:2008
Volumen:36
Número:1
Página de inicio:118
Página de fin:146
DOI: http://dx.doi.org/10.1214/009053607000000794
Título revista:Annals of Statistics
Título revista abreviado:Ann. Stat.
ISSN:00905364
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00905364_v36_n1_p118_SalibianBarrera

Referencias:

  • BRESLOW, N.E., CROWLEY, J., A large sample study of the life table and product limit estimates under random censorship (1974) Ann. Statist, 2, pp. 437-453. , MR0458674
  • BUCKLEY, J., JAMES, I., Linear regression with censored data (1979) Biometrika, 66, pp. 429-436
  • DONOHO, D. L. and HUBER, P. J. (1983). The notion of breakdown-point. In A Festschrift for Erich L. Lehmann (P. J. Bickel. K. A. Doksum and J. L. Hodges, Jr., eds.) 157-184. Wadsworth, Belmont, CA. MR0689745; EFRON, B., The two sample problem with censored (1967) data. Proc. 5th Berkeley Symp. Math. Statist. Probab, 4, pp. 831-853. , Univ. California Press, Berkeley
  • HÖSSJER, O., On the optimality of S-estimators (1992) Statist. Probab. Lett, 14, pp. 413-419. , MR1179647
  • HUBER, P. J. (1981). Robust Statistics. Wiley. New York. MR0606374; JAMES, I.R., SMITH, P.J., Consistency results for linear regression with censored data (1984) Ann. Statist, 12, pp. 590-600. , MR0740913
  • KALBFLEISCH, J. D. and PRENTICE, R. L. (1980). The Statistical Analysis of Failure Time Data. Wiley. New York. MR0570114; KAPLAN, E.L., MEIER, P., Nonparametric estimation for incomplete observations (1958) J. Amer. Statist. Assoc, 53, pp. 457-481. , MR0093867
  • LAI, T.L., YING, Z., Large sample theory of a modified Bukley-James estimator for regression analysis with censored data (1991) Ann. Statist, 19, pp. 1370-1402. , MR 1126329
  • LAI, T.L., YING, Z., A missing information principle and M-estimators in regression analysis with censored and truncated data (1994) Ann. Statist, 22, pp. 1222-1255. , MR 1311974
  • MILLER, R.G., Least squares regression with censored data (1976) Biometrika, 63, pp. 449-464. , MR0458737
  • RITOV, Y., Estimation in a linear regression model with censored data (1990) Ann. Statist, 18, pp. 303-328. , MR1041395
  • ROUSSEEUW, P.J., Least median of squares regression (1984) J. Amen Statist. Assoc, 79, pp. 871-880. , MR0770281
  • ROUSSEEUW, P. J. and LEROY, A. M. (1987). Robust Regression and Outlier Detection. Wiley, New York. MR0914792; ROUSSEEUW, P. J. and YOHAI, V. J. (1984). Robust regression by means of S-estimators. In Robust and Nonlinear Time Series Analysis (J. Franke, W. Hardie and R. D. Martin, eds.) Lecture Notes in Statist. 26 256-276. Springer, New York. MR0786313; SALIBIAN-BARRERA, M. and YOHAI, V. J. (2006). High-breakdown point robust regression with censored data. Technical Report #, Dept. Statistics, Univ. British Columbia, Vancouver, BC, Canada. Available at http://www.stat.ubc.ca/Research/TechReports/; SELLERO, C.S., MANTEIGA, W.G., VAN KEILEGOM, I., Uniform representation of product-limit integrals with applications (2005) Stand. J. Statist, 32, pp. 563-581. , MR2232343
  • STUTE, W., Consistent estimation under random censorship when covariates are present (1993) J. Multivariate Anal, 45, pp. 89-103. , MR1222607
  • STUTE, W., Distributional convergence under random censorship when covariates are present (1996) Scand. J. Statist, 23, pp. 461-471. , MR 1439707
  • STUTE, W., WANG, J.L., The strong law under random censoring (1993) Ann. Statist, 21, pp. 1591-1607. , MR1241280
  • YOHAI, V.J., High breakdown-point and high efficiency robust estimates for regression (1987) Ann. Statist, 15, pp. 642-656. , MR0888431
  • YOHAI, V.J., ZAMAR, R.H., High breakdown point and high efficiency estimates of regression by means of the minimization of an efficient scale (1988) J. Amer. Statist. Assoc, 83, pp. 406-413. , MR0971366

Citas:

---------- APA ----------
Salibian-Barrera, M. & Yohai, V.J. (2008) . High breakdown point robust regression with censored data. Annals of Statistics, 36(1), 118-146.
http://dx.doi.org/10.1214/009053607000000794
---------- CHICAGO ----------
Salibian-Barrera, M., Yohai, V.J. "High breakdown point robust regression with censored data" . Annals of Statistics 36, no. 1 (2008) : 118-146.
http://dx.doi.org/10.1214/009053607000000794
---------- MLA ----------
Salibian-Barrera, M., Yohai, V.J. "High breakdown point robust regression with censored data" . Annals of Statistics, vol. 36, no. 1, 2008, pp. 118-146.
http://dx.doi.org/10.1214/009053607000000794
---------- VANCOUVER ----------
Salibian-Barrera, M., Yohai, V.J. High breakdown point robust regression with censored data. Ann. Stat. 2008;36(1):118-146.
http://dx.doi.org/10.1214/009053607000000794