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Abstract:

We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic approximations for the quantiles of the estimate's distribution. In particular, we obtain robust asymptotic confidence intervals of minimax length.

Registro:

Documento: Artículo
Título:Optimal robust M-estimates of location
Autor:Fraiman, R.; Yohai, V.J.; Zamar, R.H.
Filiación:Departamento de Matemáticas, Universidad de San Andrés, Vito Dumas ESQ. Arias, 1644 Victoria, Argentina
Departamento de Matemáticas, Ciudad Universitaria, Pabellón 1, 1426 Buenos Aires, Argentina
Department of Statistics, University of British Columbia, 6356 Agricultural Road, Vancouver, BC V6T 1Z2, Canada
Palabras clave:M-estimates; Minimax intervals; Robust location
Año:2001
Volumen:29
Número:1
Página de inicio:194
Página de fin:223
DOI: http://dx.doi.org/10.1214/aos/996986506
Título revista:Annals of Statistics
Título revista abreviado:Ann. Stat.
ISSN:00905364
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00905364_v29_n1_p194_Fraiman

Referencias:

  • Davies, P.L., On locally uniformly linearizable high breakdown location and scale functionals (1998) Ann. Statist., 26, pp. 1103-1125
  • Hampel, F.R., The influence curve and its role in robust estimation (1974) J. Amer. Statist. Assoc., 69, pp. 383-393
  • Huber, P.J., Robust estimation of a location parameter (1964) Ann. Math. Statist., 35, pp. 73-101
  • Huber, P.J., Robust confidence limits (1968) Z. Wahrsch. Verw. Gebiete, 10, pp. 269-278
  • Huber, P.J., (1981) Robust Statistics, , Wiley, New York
  • Huber-Carol, C., (1970) Etude Asymptotique de Tests Robustes, , Ph.D. thesis, Eidgen Technische Hochschule, Zürich
  • Martin, R.D., Zamar, R.H., Efficiency-constrained bias-robust estimates of location (1993) Ann. Statist., 21, pp. 338-354
  • Rieder, H., (1994) Robust Asymptotic Statistics, , Springer, Berlin
  • Rousseeuw, P., Yohai, V.J., Robust regression by means of S-estimators (1984) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist., 26, pp. 256-272. , Springer, New York
  • Salibian-Barrera, M., (2000) Contributions to the Theory of Robust Inference, , ftp://ftp.stat.ubc.ca/pub/matias/Thesis, Ph.D. dissertation, Dept. Statistics, Univ. British Columbia, Vancouver, Canada
  • Samarov, A.M., Bounded-influence regression via local minimax mean squared error (1985) J. Amer. Statist. Assoc., 80, pp. 1032-1040
  • Stigler, S.M., Do robust estimators work with real data? (1977) Ann. Statist., 5, pp. 1055-1098

Citas:

---------- APA ----------
Fraiman, R., Yohai, V.J. & Zamar, R.H. (2001) . Optimal robust M-estimates of location. Annals of Statistics, 29(1), 194-223.
http://dx.doi.org/10.1214/aos/996986506
---------- CHICAGO ----------
Fraiman, R., Yohai, V.J., Zamar, R.H. "Optimal robust M-estimates of location" . Annals of Statistics 29, no. 1 (2001) : 194-223.
http://dx.doi.org/10.1214/aos/996986506
---------- MLA ----------
Fraiman, R., Yohai, V.J., Zamar, R.H. "Optimal robust M-estimates of location" . Annals of Statistics, vol. 29, no. 1, 2001, pp. 194-223.
http://dx.doi.org/10.1214/aos/996986506
---------- VANCOUVER ----------
Fraiman, R., Yohai, V.J., Zamar, R.H. Optimal robust M-estimates of location. Ann. Stat. 2001;29(1):194-223.
http://dx.doi.org/10.1214/aos/996986506