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Abstract:

We define a robust procedure to "correct" a regression estimate β̂0 along the directions in predictor space where the fit is worse. When β̂0 is the least median of squares estimate, the "corrected estimate" has a smaller maximum asymptotic bias under contamination, and a much better finite-sample behavior than β̂0. © 2000 Elsevier Science B.V.

Registro:

Documento: Artículo
Título:Improving bias-robustness of regression estimates through projections
Autor:Maronna, R.A.; Barrera, M.S.; Yohai, V.J.
Filiación:Departamento de Matemática, Univ. Plata C.I.C.P.B.A., C.C., La Plata, Argentina
Department of Statistics, Univ. Brit. 6356 Agric. Rd., V., Columbia, BC V6T 1Z2, Canada
Departamento de Matemática, Fac. Cie. Exact., Cd. Univ., 1428 B., Aires, Argentina
Año:2000
Volumen:47
Número:2
Página de inicio:149
Página de fin:158
DOI: http://dx.doi.org/10.1016/S0167-7152(99)00151-0
Título revista:Statistics and Probability Letters
Título revista abreviado:Stat. Probab. Lett.
ISSN:01677152
CODEN:SPLTD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01677152_v47_n2_p149_Maronna

Referencias:

  • Hawkins, D.M., The feasible set algorithm for least median of squares regression (1993) Comput. Statist. Data Anal., 16, pp. 81-101
  • He, X., A local bias property of robust tests in linear regression (1991) J. Multivariate Anal., 38, pp. 294-305
  • Maronna, R.A., Yohai, V.J., Bias-robust estimates of regression based on projections (1993) Ann. Statist., 21, pp. 965-990
  • Müller, C., Breakdown point of designed experiments (1995) J. Statist. Plann. Inference, 45, pp. 413-427
  • Rousseeuw, P.J., Leroy, A.M., (1987) Robust Regression and Outlier Detection, , Wiley, New York
  • Rousseeuw, P.J., Yohai, V.J., Robust regression by means of S-estimators (1984) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statistics, 26, pp. 256-272. , In: Franke, J., Härdle, W., Martin, R.D. (Eds.), Springer, New York
  • Salibian Barrera, M., (1994) Robust Regression Estimators, , Graduate Thesis, Faculty of Exact Sciences, University of Buenos Aires. (in Spanish)
  • 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., 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 α -quantile estimates (1993) Ann. Statist., 21, pp. 1824-1842
  • Yohai, V.J., Zamar, R.H., Optimally bounding a generalized gross error sensitivity of unbounded influence M-estimates of regression (1997) J. Statist. Plann. Inference, 57, pp. 73-92

Citas:

---------- APA ----------
Maronna, R.A., Barrera, M.S. & Yohai, V.J. (2000) . Improving bias-robustness of regression estimates through projections. Statistics and Probability Letters, 47(2), 149-158.
http://dx.doi.org/10.1016/S0167-7152(99)00151-0
---------- CHICAGO ----------
Maronna, R.A., Barrera, M.S., Yohai, V.J. "Improving bias-robustness of regression estimates through projections" . Statistics and Probability Letters 47, no. 2 (2000) : 149-158.
http://dx.doi.org/10.1016/S0167-7152(99)00151-0
---------- MLA ----------
Maronna, R.A., Barrera, M.S., Yohai, V.J. "Improving bias-robustness of regression estimates through projections" . Statistics and Probability Letters, vol. 47, no. 2, 2000, pp. 149-158.
http://dx.doi.org/10.1016/S0167-7152(99)00151-0
---------- VANCOUVER ----------
Maronna, R.A., Barrera, M.S., Yohai, V.J. Improving bias-robustness of regression estimates through projections. Stat. Probab. Lett. 2000;47(2):149-158.
http://dx.doi.org/10.1016/S0167-7152(99)00151-0