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A necessary power divergence type family tests of multivariate normality

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Batsidis, Apostolos and Martin, Nirian and Pardo Llorente, Leandro and Zografos, Konstantinos (2013) A necessary power divergence type family tests of multivariate normality. Communications in Statistics - Simulation and Computation, 42 (10). pp. 2253-2271. ISSN 0361-0918

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Official URL: http://www.tandfonline.com/doi/pdf/10.1080/03610918.2012.697238


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Abstract

In a recent article, Cardoso de Oliveira and Ferreira have proposed a multivariate extension of the univariate chi-squared normality test, using a known result for the distribution of quadratic forms in normal variables. In this article, we propose a family of power divergence type test statistics for testing the hypothesis of multinormality. The proposed family of test statistics includes as a particular case the test proposed by Cardoso de Oliveira and Ferreira. We assess the performance of the new family of test statistics by using Monte Carlo simulation. In this context, the type I error rates and the power of the tests are studied, for important family members. Moreover, the performance of significant members of the proposed test statistics are compared with the respective performance of a multivariate normality test, proposed recently by Batsidis and Zografos. Finally, two well-known data sets are used to illustrate the method developed in this article as well as the specialized test of multivariate normality proposed by Batsidis and Zografos.


Item Type:Article
Uncontrolled Keywords:Goodness of fit; Monte Carlo study; Multivariate normality test; Power divergence; Song's measure
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:21222
Deposited On:06 May 2013 10:22
Last Modified:06 Aug 2018 11:11

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