A goodness-of-fit test for elliptical distributions with diagnostic capabilities

This paper develops a test of goodness-of-fit for elliptical distributions. The test is invariant to affine-linear transformations and has a convenient expression that can be broken into components containing diagnostic information to be used to identify possible departures when the test rejects. Th...

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Bibliographic Details
Published in:Journal of multivariate analysis 2020-07, Vol.178, p.104602, Article 104602
Main Authors: Ducharme, Gilles R., Lafaye de Micheaux, Pierre
Format: Article
Language:English
Subjects:
Diagnostic information
Elliptical distribution
Mathematics
Multivariate Laplace distribution
Multivariate logistic distribution
Multivariate normal distribution
Smooth goodness-of-fit test
Statistics
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Summary:This paper develops a test of goodness-of-fit for elliptical distributions. The test is invariant to affine-linear transformations and has a convenient expression that can be broken into components containing diagnostic information to be used to identify possible departures when the test rejects. The test is developed for the bivariate Laplace, logistic and Pearson type II distributions, as well as the multivariate normal for which the R package ECGofTestDx is available on the CRAN. A simulation shows the usefulness of the diagnostic tools.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2020.104602