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Abstract:

This paper provides a comparative sensitivity analysis of one-step Newton-Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by ε-contamination of the model. These bounds yield breakdown points and local rates of convergence of the bias as ε decreases to zero. We treat a unified class of Newton-Raphson estimators, including one-step versions of the well-known Schweppe, Mallows and Hill-Ryan GM estimators. Of the three well-known types, the Hill-Ryan form emerges as the most stable in terms of one-step estimation. The Schweppe form is susceptible to a breakdown of the Hessian matrix. For this reason it fails to improve on the local stability of the initial estimator, and it may lead to falsely optimistic estimates of precision.

Registro:

Documento: Artículo
Título:Functional stability of one-step GM-estimators in approximately linear regression
Autor:Simpson, D.G.; Yohai, V.J.
Filiación:University of Illinois, Urbana-Champaign, IL, United States
Department of Statistics, University of Illinois, 101 Illini Hall, 725 South Wright Street, Champaign, IL 61820, United States
Departamento de Matematicas, Ciudad Universitaria Pabellon 1, 1426 Buenos Aires, Argentina
Palabras clave:Breakdown point; Maximum bias function; Newton-Raphson; Robust statistics; Weighted least squares
Año:1998
Volumen:26
Número:3
Página de inicio:1147
Página de fin:1169
DOI: http://dx.doi.org/10.1214/aos/1024691092
Título revista:Annals of Statistics
Título revista abreviado:Ann. Stat.
ISSN:00905364
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00905364_v26_n3_p1147_Simpson

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Citas:

---------- APA ----------
Simpson, D.G. & Yohai, V.J. (1998) . Functional stability of one-step GM-estimators in approximately linear regression. Annals of Statistics, 26(3), 1147-1169.
http://dx.doi.org/10.1214/aos/1024691092
---------- CHICAGO ----------
Simpson, D.G., Yohai, V.J. "Functional stability of one-step GM-estimators in approximately linear regression" . Annals of Statistics 26, no. 3 (1998) : 1147-1169.
http://dx.doi.org/10.1214/aos/1024691092
---------- MLA ----------
Simpson, D.G., Yohai, V.J. "Functional stability of one-step GM-estimators in approximately linear regression" . Annals of Statistics, vol. 26, no. 3, 1998, pp. 1147-1169.
http://dx.doi.org/10.1214/aos/1024691092
---------- VANCOUVER ----------
Simpson, D.G., Yohai, V.J. Functional stability of one-step GM-estimators in approximately linear regression. Ann. Stat. 1998;26(3):1147-1169.
http://dx.doi.org/10.1214/aos/1024691092