Robust analysis of variance for a randomized block design

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 cla...

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Detalles Bibliográficos
Autores principales:	García Ben, M., Yohai, V.
Formato:	JOUR
Materias:	M-estimators randomized block design Robust estimation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03610926_v21_n6_p1779_GarciaBen
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_03610926_v21_n6_p1779_GarciaBen2023-10-03T15:26:41Z Robust analysis of variance for a randomized block design García Ben, M. Yohai, V. M-estimators randomized block design Robust estimation 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03610926_v21_n6_p1779_GarciaBen
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	M-estimators randomized block design Robust estimation
spellingShingle	M-estimators randomized block design Robust estimation García Ben, M. Yohai, V. Robust analysis of variance for a randomized block design
topic_facet	M-estimators randomized block design Robust estimation
description	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.
format	JOUR
author	García Ben, M. Yohai, V.
author_facet	García Ben, M. Yohai, V.
author_sort	García Ben, M.
title	Robust analysis of variance for a randomized block design
title_short	Robust analysis of variance for a randomized block design
title_full	Robust analysis of variance for a randomized block design
title_fullStr	Robust analysis of variance for a randomized block design
title_full_unstemmed	Robust analysis of variance for a randomized block design
title_sort	robust analysis of variance for a randomized block design
url	http://hdl.handle.net/20.500.12110/paper_03610926_v21_n6_p1779_GarciaBen
work_keys_str_mv	AT garciabenm robustanalysisofvarianceforarandomizedblockdesign AT yohaiv robustanalysisofvarianceforarandomizedblockdesign
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Robust analysis of variance for a randomized block design

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