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Abstract:

A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a new scale estimate, τ, applied to the residuals. Asymptotically, a τ estimate is equivalent to an M estimate with a ψ function given by a weighted average of two ψ functions, one corresponding to a very robust estimate and the other to a highly efficient estimate. The weights are adaptive and depend on the underlying error distribution. We prove consistency and asymptotic normality and give a convergent iterative computing algorithm. Finally, we compare the biases produced by gross error contamination in the τ estimates and optimal bounded-influence estimates. © 1976 Taylor & Francis Group, LLC.

Registro:

Documento: Artículo
Título:High breakdown-point estimates of regression by means of the minimization of an efficient scale
Autor:Yohai, V.J.; Zamar, R.H.
Filiación:Departamento de Matematica, Facultad de C. Exactas y Naturales, Universidad de Buenos Aires, Pabellon 1, Buenos Aires, 1428, Argentina
Centro de Estudios de Macroeconomia de Argentina, Virrey del Pino 3210, Buenos Aires, 1428, Argentina
Department of Statistics, University of British Columbia, Vancouver, BC, V6T 1W5, Canada
Palabras clave:Bias robustness; High efficiency; Robust estimate
Año:1988
Volumen:83
Número:402
Página de inicio:406
Página de fin:413
DOI: http://dx.doi.org/10.1080/01621459.1988.10478611
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v83_n402_p406_Yohai

Referencias:

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  • Yohai, V.J., (1985) High Breakdown-Point and High Efficiency Robust Estimates for Regression, , Technical Report 66, University of Washington, Dept. of Statistics
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Citas:

---------- APA ----------
Yohai, V.J. & Zamar, R.H. (1988) . High breakdown-point estimates of regression by means of the minimization of an efficient scale. Journal of the American Statistical Association, 83(402), 406-413.
http://dx.doi.org/10.1080/01621459.1988.10478611
---------- CHICAGO ----------
Yohai, V.J., Zamar, R.H. "High breakdown-point estimates of regression by means of the minimization of an efficient scale" . Journal of the American Statistical Association 83, no. 402 (1988) : 406-413.
http://dx.doi.org/10.1080/01621459.1988.10478611
---------- MLA ----------
Yohai, V.J., Zamar, R.H. "High breakdown-point estimates of regression by means of the minimization of an efficient scale" . Journal of the American Statistical Association, vol. 83, no. 402, 1988, pp. 406-413.
http://dx.doi.org/10.1080/01621459.1988.10478611
---------- VANCOUVER ----------
Yohai, V.J., Zamar, R.H. High breakdown-point estimates of regression by means of the minimization of an efficient scale. J. Am. Stat. Assoc. 1988;83(402):406-413.
http://dx.doi.org/10.1080/01621459.1988.10478611