K-sample tests for equality of variances of random fuzzy sets

Authors:
Ana Belén Ramos-Guajardo;María Asunción Lubiano
Affiliations:
European Centre for Soft Computing, C/ Gonzalo Gutiérrez Quirós s/n, Mieres-Asturias 33600, Spain;Dpto. de Estadística, I.O y D.M., C/ Calvo Sotelo s/n, Oviedo 33007, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2012

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Abstract

The problem of testing equality of variances often arises when distributions of random variables are compared or linear models between them are considered. The usual tests for variances given normality of the underlying populations are highly non-robust to non-normality and are strongly dependent on the kurtosis. Some alternative formulations of Levene's test statistic for testing the homoscedasticity have been shown to be powerful and robust under non-normality. On the basis of Levene's classical procedure, a test for the equality of variances of k fuzzy-valued random elements is developed. Accordingly, consistent asymptotic and bootstrap tests are established and their empirical behaviour is analyzed by means of extensive simulation studies. In addition, the proposed test is compared with a Bartlett-type test. A case-study illustrating the applicability of the procedure is presented.