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

• Published in: Computational statistics & data analysis 2012-04, Vol.56 (4), p.956-966
• Main Authors: Ramos-Guajardo, Ana Belén, Lubiano, María Asunción
• Format: Article
• Language: English
• Subjects: [formula omitted] metric; Equality of variances; Equality of variances Levene’s test Random fuzzy set Hypothesis testing Dθφ metric; Hypothesis testing; Levene’s test; Random fuzzy set
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.11.025

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.