{"title":"用最大熵拟合copula。","authors":"Milan Bubák, Mirko Navara","doi":"10.3390/e27010087","DOIUrl":null,"url":null,"abstract":"<p><p>We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11765149/pdf/","citationCount":"0","resultStr":"{\"title\":\"Fitting Copulas with Maximal Entropy.\",\"authors\":\"Milan Bubák, Mirko Navara\",\"doi\":\"10.3390/e27010087\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.</p>\",\"PeriodicalId\":11694,\"journal\":{\"name\":\"Entropy\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2025-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11765149/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entropy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3390/e27010087\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e27010087","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.
期刊介绍：
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.
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