The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis |
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| Authors: | Mattias Villani Rolf Larsson |
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| Institution: | 1. Research Division, Sveriges Riksbank and Department of Statistics , Stockholm University , Stockholm , Sweden mattias.villani@riksbank.se;3. Department of Information Science , Uppsala University , Uppsala , Sweden |
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| Abstract: | The multivariate split normal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the principal axes. This article derives some properties for this distribution, including its moment generating function, multivariate skewness, and kurtosis, and discusses its role as a population model for asymmetric principal components analysis. Maximum likelihood estimators and a complete Bayesian analysis, including inference on the number of skewed dimensions and their directions, are presented. |
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| Keywords: | Bayesian inference Estimation Maximum likelihood Multivariate analysis Skewness Statistical distribution |
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