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Abstract:

This paper introduces a new class of robust estimators for the linear regression model. They are weighted least squares estimators, with weights adaptively computed using the empirical distribution of the residuals of an initial robust estimator. It is shown that under certain general conditions the asymptotic breakdown points of the proposed estimators are not less than that of the initial estimator, and the finite sample breakdown point can be at most 1/n less. For the special case of the least median of squares as initial estimator, hard rejection weights and normal errors and carriers, the maximum bias function of the proposed estimators for point-mass contaminations is numerically computed, with the result that there is almost no worsening of bias. Moreover - and this is the original contribution of this paper - if the errors are normally distributed and under fairly general conditions on the design the proposed estimators have full asymptotic efficiency. A Monte Carlo study shows that they have better behavior than the initial estimators for finite sample sizes.

Registro:

Documento: Artículo
Título:A class of robust and fully efficient regression estimators
Autor:Gervini, D.; Yohai, V.J.
Filiación:Department of Biostatistics, University of Zurich, Sumatrastrasse 30, CH-8006 Zurich, Switzerland
Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Pabellón 1, 1428 Buenos Aires, Argentina
Palabras clave:Adaptive estimation; Efficient estimation; Maximum breakdown point; Weighted least squares
Año:2002
Volumen:30
Número:2
Página de inicio:583
Página de fin:616
DOI: http://dx.doi.org/10.1214/aos/1021379866
Título revista:Annals of Statistics
Título revista abreviado:Ann. Stat.
ISSN:00905364
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00905364_v30_n2_p583_Gervini

Referencias:

  • Adrover, J., Bianco, A., Yohai, V.J., Approximate τ-estimates for linear regression based on subsampling of elemental sets (2001) Statistics in Genetics and in the Environmental Sciences, pp. 141-151. , L. T. Femholz, S. Morgenthaler and W. Stahel, eds. Birkäuser, Basel
  • Agostinelli, C., Markatou, M., A one-step robust estimator for regression based on the weighted likelihood reweighting scheme (1998) Statist. Probab. Lett., 37, pp. 341-350
  • Davies, L., The asymptotics of S-estimators in the linear regression model (1990) Ann. Statist., 18, pp. 1651-1675
  • Donoho, D.L., Huber, P.J., The notion of breakdown point (1983) A Festschrift for Erich L. Lehmann, pp. 157-184. , P. J. Bickel, K. A. Doksum and J. L. Hodges, Jr., eds. Wadsworth, Belmont, CA
  • Gervini, D., Yohai, V.J., (2000) A Class of Robust and Fully Efficient Regression Estimators, , Unpublished manuscript
  • Hampel, F.R., Beyond location parameters: Robust concepts and methods (with discussion) (1975) Bull. ISI, 46, pp. 375-391
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust Statistics: The Approach Based on Influence Functions, , Wiley, New York
  • He, X., Portnoy, S., Reweighted LS estimators converge at the same rate as the initial estimator (1992) Ann. Statist., 20, pp. 2161-2167
  • Hössjer, O., On the optimality of S-estimators (1992) Statist. Probab. Lett., 14, pp. 413-419
  • Martin, R.D., Yohai, V.J., Zamar, R.H., Min-max bias robust regression (1989) Ann. Statist., 17, pp. 1608-1630
  • Pollard, D., (1990) Empirical Processes: Theory and Applications, , IMS, Hayward, CA
  • Rousseeuw, P.J., Least median of squares regression (1984) J. Amer. Statist. Assoc., 79, pp. 871-880
  • Rousseeuw, P.J., Leroy, A., (1987) Robust Regression and Outlier Detection, , Wiley, New York
  • Rousseeuw, P.J., Yohai, V., Robust regression by means of 5-estimators (1984) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist., 26, pp. 256-272. , Springer, New York
  • Simpson, D.G., Yohai, V.J., Functional stability of one-step GM-estimators in approximately linear regression (1998) Ann. Statist., 26, pp. 1147-1169
  • Yohai, V.J., High breakdown-point and high efficiency robust estimates for regression (1987) Ann. Statist., 15, pp. 642-656
  • Yohai, V.J., Zamar, R.H., High breakdown-point estimates of regression by means of the minimization of an efficient scale (1988) J. Amer. Statist. Assoc., 83, pp. 406-413
  • Yohai, V.J., Zamar, R.H., A minimax-bias property of the least a-quantile estimates (1993) Ann. Statist., 21, pp. 1824-1842

Citas:

---------- APA ----------
Gervini, D. & Yohai, V.J. (2002) . A class of robust and fully efficient regression estimators. Annals of Statistics, 30(2), 583-616.
http://dx.doi.org/10.1214/aos/1021379866
---------- CHICAGO ----------
Gervini, D., Yohai, V.J. "A class of robust and fully efficient regression estimators" . Annals of Statistics 30, no. 2 (2002) : 583-616.
http://dx.doi.org/10.1214/aos/1021379866
---------- MLA ----------
Gervini, D., Yohai, V.J. "A class of robust and fully efficient regression estimators" . Annals of Statistics, vol. 30, no. 2, 2002, pp. 583-616.
http://dx.doi.org/10.1214/aos/1021379866
---------- VANCOUVER ----------
Gervini, D., Yohai, V.J. A class of robust and fully efficient regression estimators. Ann. Stat. 2002;30(2):583-616.
http://dx.doi.org/10.1214/aos/1021379866