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Abstract:

In this paper simultaneous redescending M-estimates for scale and regression parameters are properly defined. The breakdown point of this estimates is derived. It is proved that these estimates are asymptotically normal and their covariance matrix is obtained. These results show that simultaneous redescending M-estimates may combine high breakdown point and high asymptotic efficiency under normal errors.

Registro:

Documento: Artículo
Título:Simultaneous redescending M-estimates for regression and scale
Autor:Adrover, J.G.; Yohai, V.J.
Filiación:Fac. de Matemática, Astronomía y Física, Universidad Nacional de Cordoba, 5000 Cordoba, Argentina
Dpto. de Matemática, Fac. de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Breakdown point; Efficiency; Linear regression; Robustness; Simultaneous m- Estimates
Año:2000
Volumen:29
Número:2
Página de inicio:243
Página de fin:262
Título revista:Communications in Statistics - Theory and Methods
Título revista abreviado:Commun Stat Theory Methods
ISSN:03610926
CODEN:CSTMD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v29_n2_p243_Adrover

Referencias:

  • Adrover, J.G., Bianco, A.M., Breakdown and asymptotic properties of resampled τ-estimates (1995) Working Paper No. 95-29, , Dept. of Statistics and Econometrics. Universidad Carlos III de Madrid
  • Adrover, J.G., Yohai, V.J., Simultaneous redescending M-estimates for regression and scale (1999) Technical Report No. #186, 186. , Dept. of Statistics. University of British Columbia
  • Brown, L.D., Purves, R., Measurable Selection of Extrema (1973) Ann. Statist., 1, pp. 902-912
  • Davies, P.L., Aspects of Robust Linear Regression (1993) Ann. Statist., 4, pp. 1843-1899
  • Donoho, D.L., Huber, P.J., The notion of breakdown point (1983) A Festschrift to Erich Lehmann, pp. 157-184. , P.J. Bickel, K. Doksum and J.L. Hodges, Jr., eds., Wadsworth, Belmont
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust Statistics: The Approach Based on Influence Functions, , Wiley, New York
  • Hössjer, O., On the optimality of S-estimators (1992) Stat. Probab. Lett., 14, pp. 413-419
  • Huber, P.J., (1981) Robust Statistics, , Wiley, New York
  • Huber, P.J., Finite Sample Breakdown of M- and P-estimators (1984) Ann. Statist., 12, pp. 119-126
  • Maronna, R.A., Bustos, O.H., Yohai, V.J., Bias- and efficiency-robustness of general M-estimators for regression with random carriers (1979) Lecture Notes in Mathematics, 757. , Smoothing Techniques for Curve Estimation, eds. T. Gasser and J. M. Rosenblatt, Springer-Verlag, New York
  • Mendes, B., Tyler, D.E., Constrained M-estimation for Regression (1996) Lecture Notes in Statistics, 109, pp. 299-320. , Robust statistics, data analysis and Computer intensive Models, ed. H. Rieder, Springer-Verlag, New York
  • Rousseeuw, P.J., Least median of squares regression (1984) J. Am. Statist. Assoc., 79, pp. 871-880
  • Rousseeuw, P.J., Yohai, V.J., Robust Regression by means of S-estimators (1984) Lecture Notes in Statistics, 26, pp. 256-272. , Robust and nonlinear time series analysis, eds. J. Franke, W. Härdle and R.D. Martin, Springer-Verlag, New York
  • Simpson, D.G., Ruppert, D., Carroll, R.J., On one-step GM estimates and stability of inferences in linear regression (1992) J. Am. Statist. Assoc., 87, pp. 439-450
  • Yang, J.J., Van Ness, J.W., Breakdown Points for Redescending M-estimates of Location (1995) Commun. Statist.-Theory Meth., 24, pp. 1769-1787
  • Yohai, V.J., High Breakdown-Point and High Efficiency 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. Am. 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

Citas:

---------- APA ----------
Adrover, J.G. & Yohai, V.J. (2000) . Simultaneous redescending M-estimates for regression and scale. Communications in Statistics - Theory and Methods, 29(2), 243-262.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v29_n2_p243_Adrover [ ]
---------- CHICAGO ----------
Adrover, J.G., Yohai, V.J. "Simultaneous redescending M-estimates for regression and scale" . Communications in Statistics - Theory and Methods 29, no. 2 (2000) : 243-262.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v29_n2_p243_Adrover [ ]
---------- MLA ----------
Adrover, J.G., Yohai, V.J. "Simultaneous redescending M-estimates for regression and scale" . Communications in Statistics - Theory and Methods, vol. 29, no. 2, 2000, pp. 243-262.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v29_n2_p243_Adrover [ ]
---------- VANCOUVER ----------
Adrover, J.G., Yohai, V.J. Simultaneous redescending M-estimates for regression and scale. Commun Stat Theory Methods. 2000;29(2):243-262.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v29_n2_p243_Adrover [ ]