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Abstract:

In this paper we study the asymptotic theory of M-estimates and their associated tests for a one-factor experiment in a randomized block design. In this case one natural asymptotic theory corresponds to leaving the number of treatments fixed and letting the number of blocks tend to infinity. The classic asymptotic theory of M-estimates does not apply here, because the number of parameters and the number of observations are of the same order. In this paper we prove the consistency and asymptotic normality of the estimators of the treatment effects. It turns out that the asymptotic covariance matrix of the treatment effects estimators differs from the one derived from the classic theory of M-estimates for the linear model with a fixed number of parameters. We also study a test for treatment effects derived from M-estimates and we compare by Monte Carlo simulation the efficiency of this test with respect to the F-test, the Friedman test and the test based on aligned ranks. © 1992, Taylor & Francis Group, LLC. All rights reserved.

Registro:

Documento: Artículo
Título:Robust analysis of variance for a randomized block design
Autor:García Ben, M.; Yohai, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, U.B.A., Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas, U.B.A., Conicet, Buenos Aires, Argentina
Palabras clave:M-estimators; randomized block design; Robust estimation
Año:1992
Volumen:21
Número:6
Página de inicio:1779
Página de fin:1798
DOI: http://dx.doi.org/10.1080/03610929208830878
Título revista:Communications in Statistics - Theory and Methods
Título revista abreviado:Commun Stat Theory Methods
ISSN:03610926
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03610926_v21_n6_p1779_GarciaBen

Referencias:

  • Billingsley, A., (1968) Convergence of Probability Measures, , New York: Wiley
  • Huber, P.J., Robust estimation of a location parameter (1964) Ann. Math. Statist, 35, pp. 73-101
  • Huber, P.J., Robust regression: asymptotics, conjectures and Monte Carlo (1973) Annals of Statistics, 1, pp. 799-821
  • Huber, P.J., (1981) Robust Statistics, , New York: Wiley
  • Lehmann, E.L., (1975) Nonparametrics statistical methods based on ranks, , San Francisco: Holden-Day
  • Mammen, E., Assymptotics with increasing dimension for robust regression with applications to the bootstrap (1989) Annals of Statistics, 17, pp. 382-400
  • Portnoy, S., Asymptotic behavior of M-estimators of p regression parameters when p2/n is large. I. Consistency (1984) Annals of Statistics, 12, pp. 1298-1309
  • Portnoy, S., Asymptotic behavior of M-estimators of p regression parameters when p2/n is large. II. Asymptotic normality (1985) Annals of Statistics, 13, pp. 1403-1417
  • Puri, M.L., Sen, P.K., (1971) Nonparametric Methods in Multivariate Analysis, , New York: Wiley
  • Schrader, R.M., Hettmansperger, T.P., Robust analysis of variance based upon a likelihood ratio criterion (1980) Biometrika, 67, pp. 93-101
  • Schrader, R.M., Mc Kean, J.W., Robust analysis of variance (1979) Communications in Statistics, A6, pp. 879-894
  • Yohai, V.J., High breakdown point and high efficciency robust estimates for regression. Technical Report (1985) Dept. Statistics, Univ, 66. , Washington, Seattle
  • Yohai, V.J., Maronna, R.A., Asymptotic behavior of M-estimators for the linear model (1979) Annals of Statistics, 7, pp. 258-268

Citas:

---------- APA ----------
García Ben, M. & Yohai, V. (1992) . Robust analysis of variance for a randomized block design. Communications in Statistics - Theory and Methods, 21(6), 1779-1798.
http://dx.doi.org/10.1080/03610929208830878
---------- CHICAGO ----------
García Ben, M., Yohai, V. "Robust analysis of variance for a randomized block design" . Communications in Statistics - Theory and Methods 21, no. 6 (1992) : 1779-1798.
http://dx.doi.org/10.1080/03610929208830878
---------- MLA ----------
García Ben, M., Yohai, V. "Robust analysis of variance for a randomized block design" . Communications in Statistics - Theory and Methods, vol. 21, no. 6, 1992, pp. 1779-1798.
http://dx.doi.org/10.1080/03610929208830878
---------- VANCOUVER ----------
García Ben, M., Yohai, V. Robust analysis of variance for a randomized block design. Commun Stat Theory Methods. 1992;21(6):1779-1798.
http://dx.doi.org/10.1080/03610929208830878