{"title":"Quadratic transformation of multivariate aggregation functions","authors":"Prakassawat Boonmee, S. Tasena","doi":"10.1515/demo-2020-0015","DOIUrl":null,"url":null,"abstract":"Abstract In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"8 1","pages":"254 - 261"},"PeriodicalIF":0.8000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2020-0015","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dependence Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/demo-2020-0015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.
期刊介绍：
The journal Dependence Modeling aims at providing a medium for exchanging results and ideas in the area of multivariate dependence modeling. It is an open access fully peer-reviewed journal providing the readers with free, instant, and permanent access to all content worldwide. Dependence Modeling is listed by Web of Science (Emerging Sources Citation Index), Scopus, MathSciNet and Zentralblatt Math. The journal presents different types of articles: -"Research Articles" on fundamental theoretical aspects, as well as on significant applications in science, engineering, economics, finance, insurance and other fields. -"Review Articles" which present the existing literature on the specific topic from new perspectives. -"Interview articles" limited to two papers per year, covering interviews with milestone personalities in the field of Dependence Modeling. The journal topics include (but are not limited to): -Copula methods -Multivariate distributions -Estimation and goodness-of-fit tests -Measures of association -Quantitative risk management -Risk measures and stochastic orders -Time series -Environmental sciences -Computational methods and software -Extreme-value theory -Limit laws -Mass Transportations
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