A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Characteristics of multivariate distributions and the invariant coordinate system
Tekijät: Ilmonen P, Nevalainen J, Oja H
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2010
Journal: Statistics and Probability Letters
Tietokannassa oleva lehden nimi: STATISTICS & PROBABILITY LETTERS
Lehden akronyymi: STAT PROBABIL LETT
Numero sarjassa: 23-24
Vuosikerta: 80
Numero: 23-24
Aloitussivu: 1844
Lopetussivu: 1853
Sivujen määrä: 10
ISSN: 0167-7152
DOI: https://doi.org/10.1016/j.spl.2010.08.010
Tiivistelmä
We consider a semiparametric multivariate location-scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis. (c) 2010 Elsevier B.V All rights reserved.
We consider a semiparametric multivariate location-scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis. (c) 2010 Elsevier B.V All rights reserved.
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