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http://hdl.handle.net/1942/38045
Title: | Flexible asymmetric multivariate distributions based on two-piece univariate distributions | Authors: | BAILLIEN, Jonas Gijbels, Irene VERHASSELT, Anneleen |
Issue Date: | 2023 | Publisher: | SPRINGER HEIDELBERG | Source: | Annals of the Institute of Statistical Mathematics, 75 (1), p. 159-200 | Abstract: | Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions, grouped under the name "skewed distributions", have been developed to specifically cope with asymmetric data. In this paper, we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These are members of a flexible family of univariate asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are supported by a simulation study confirming the developed theoretical results, and some data examples to illustrate practical applicability. | Notes: | Gijbels, I (corresponding author), Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B,Box 2400, B-3001 Heverlee, Belgium.; Gijbels, I (corresponding author), Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, Celestijnenlaan 200B,Box 2400, B-3001 Heverlee, Belgium. irene.gijbels@kuleuven.be |
Keywords: | Affine combination;Maximum likelihood estimation;Multivariate skew distribution | Document URI: | http://hdl.handle.net/1942/38045 | ISSN: | 0020-3157 | e-ISSN: | 1572-9052 | DOI: | 10.1007/s10463-022-00842-6 | ISI #: | 000836359500002 | Rights: | The Institute of Statistical Mathematics, Tokyo 2022 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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s10463-022-00842-6.pdf Restricted Access | Published version | 2.64 MB | Adobe PDF | View/Open Request a copy |
PaperBGV.pdf | Peer-reviewed author version | 785.45 kB | Adobe PDF | View/Open |
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