Tests of multinormality based on location vectors and scatter matrices

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dc.contributor.author Kankainen, Annaliisa
dc.contributor.author Taskinen, Sara
dc.contributor.author Oja, Hannu
dc.date.accessioned 2012-11-30T12:01:13Z
dc.date.available 2012-11-30T12:01:13Z
dc.date.issued 2007 fi
dc.identifier.citation Kankainen, A., Taskinen, S., & Oja, H. (2007). Tests of multinormality based on location vectors and scatter matrices. <em>Stat. Methods Appl.</em>, 16 (3), 357-379. <a href="http://dx.doi.org/10.1007/s10260-007-0045-9">doi:10.1007/s10260-007-0045-9</a> fi
dc.identifier.issn 1618-2510
dc.identifier.other TUTKAID_28711
dc.identifier.uri http://hdl.handle.net/123456789/40494
dc.description.abstract Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is developed to provide approximate null distributions as well as to consider asymptotic efficiencies. Limiting Pitman efficiencies for contiguous sequences of contaminated normal distributions are calculated and the efficiencies are compared to those of the classical tests by Mardia. Simulations are used to compare finite sample efficiencies. The theory is also illustrated by an example. fi
dc.language.iso eng
dc.publisher Springer
dc.relation.ispartofseries Statistical Methods and Applications
dc.rights © Springer. This is a manuscript of an article whose final and definitive form has been published by Springer.
dc.rights openAccess fi
dc.subject.other Affine invariance fi
dc.subject.other Kurtosis fi
dc.subject.other Pitman efficiency fi
dc.subject.other Skewness fi
dc.title Tests of multinormality based on location vectors and scatter matrices fi
dc.type Article en
dc.identifier.urn URN:NBN:fi:jyu-201211293125
dc.subject.kota 112
dc.contributor.laitos Matematiikan ja tilastotieteen laitos fi
dc.contributor.laitos Department of Mathematics and Statistics en
dc.contributor.oppiaine tilastotiede fi
dc.identifier.volume 16
dc.identifier.issue 3
jyx.tutka.pagetopage 357-379
dc.type.uri http://purl.org/eprint/type/SubmittedJournalArticle
dc.identifier.doi 10.1007/s10260-007-0045-9
dc.date.updated 2012-11-29T10:40:04Z
dc.description.version Manuscript
eprint.status http://purl.org/eprint/type/status/PeerReviewed

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