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Abstract:

In this paper, we study the Huber M-estimator for location when they are computed by a class of numerical iterative procedures. This class includes the usual method of Newton-Raphson, iterated weighted least squares and iterated winsorization. We show that under mild conditions, the numerical iterative procedures converge and the resulting estimators are consistent and asymptotically normal. © 1979 Sociedade Brasileira de Matemática.

Registro:

Documento: Artículo
Título:Asymptotic behavior of iterative M-estimartors for location
Autor:Klein, R.; Yohai, V.J.
Filiación:Instituto de Matemática Pura e Aplicada, Rua Luiz de Camões, 68, Rio de Janeiro, 20.060, RJ, Brazil
Departamento de Matematicas, Facultad de Ciencias Exactas y Naturales, Pabellón 1, Ciudad Universitaria, Buenos Aires, Argentina
Año:1979
Volumen:10
Número:1
Página de inicio:27
Página de fin:42
DOI: http://dx.doi.org/10.1007/BF02588338
Título revista:Boletim da Sociedade Brasileira de Matemática
Título revista abreviado:Bol. Soc. Bras. Mat
ISSN:01003569
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01003569_v10_n1_p27_Klein

Referencias:

  • Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1972). Robust Estimates of Location: Survey and Advances, Princeton Univ. Press; Berk, R., A Special Structure and Equivariant Estimation (1967) The Annals of Mathematical Statistics, 38, pp. 1436-1445
  • Bickel, P.J., One-step Huber Estimates in the Linear Model (1975) Journal of the American Statistical Association, 70, pp. 428-434
  • Collins, J.R., Robust Estimation of a Location Parameter in the Presence of Asymmetry (1976) The Annals of Statistics, 4, pp. 68-85
  • Dutter, R., (1975) Robust Regression: Different Approaches to Numerical Solutions and Algorithms, , Research Report, n.o 6, Fachgruppe für Statistik, ETH, Zurich
  • Hampel, F.R., (1968) Contributions to the Theory of Robust Estimation, , Univ. of California, Berkeley
  • Hampel, F.R., The Influence Curve and Its Role in Robust Estimation (1974) Journal of the American Statistical Association, 69, pp. 383-393
  • Huber, P.J., Robust Estimation of a Location Parameter (1964) The Annals of Mathematical Statistics, 35, pp. 73-101
  • Huber, P.J., The Behavior of Maximum Likelihood estimates Under Nonstandard Conditions (1977) Proc. Fifth Berkeley Symp. Math. Statist. Prob., 1, pp. 221-223
  • Huber, P.J., Robust Regression: Asymptotics, Conjectures and Monte Carlo (1973) The Annals of Statistics, 1, pp. 799-821
  • Relles, D. A. (1968). Robust Regression by Modified Least Squares. Ph. D. Dissertation. Yale University; Yohai, V.J., Robust Estimation in the Linear Model (1974) The Annals of Statistics, 2, pp. 562-567
  • Yohai, V. J. and Maronna, R. A. (1976). Asymptotic Behavior of M-estimators for the Linear Model, (To appear)

Citas:

---------- APA ----------
Klein, R. & Yohai, V.J. (1979) . Asymptotic behavior of iterative M-estimartors for location. Boletim da Sociedade Brasileira de Matemática, 10(1), 27-42.
http://dx.doi.org/10.1007/BF02588338
---------- CHICAGO ----------
Klein, R., Yohai, V.J. "Asymptotic behavior of iterative M-estimartors for location" . Boletim da Sociedade Brasileira de Matemática 10, no. 1 (1979) : 27-42.
http://dx.doi.org/10.1007/BF02588338
---------- MLA ----------
Klein, R., Yohai, V.J. "Asymptotic behavior of iterative M-estimartors for location" . Boletim da Sociedade Brasileira de Matemática, vol. 10, no. 1, 1979, pp. 27-42.
http://dx.doi.org/10.1007/BF02588338
---------- VANCOUVER ----------
Klein, R., Yohai, V.J. Asymptotic behavior of iterative M-estimartors for location. Bol. Soc. Bras. Mat. 1979;10(1):27-42.
http://dx.doi.org/10.1007/BF02588338