Jonas Baillien, Irène Gijbels, Anneleen Verhasselt
{"title":"Flexible asymmetric multivariate distributions based on two-piece univariate distributions","authors":"Jonas Baillien, Irène Gijbels, Anneleen Verhasselt","doi":"10.1007/s10463-022-00842-6","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"75 1","pages":"159 - 200"},"PeriodicalIF":0.8000,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-022-00842-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.