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A topological proof of Sklar’s theorem in arbitrary dimensions 任意维的斯克拉定理的拓扑证明
IF 0.7
Dependence Modeling Pub Date : 2021-01-21 DOI: 10.1515/demo-2022-0103
F. Benth, G. Nunno, Dennis Schroers
{"title":"A topological proof of Sklar’s theorem in arbitrary dimensions","authors":"F. Benth, G. Nunno, Dennis Schroers","doi":"10.1515/demo-2022-0103","DOIUrl":"https://doi.org/10.1515/demo-2022-0103","url":null,"abstract":"Abstract Copulas are appealing tools in multivariate probability theory and statistics. Nevertheless, the transfer of this concept to infinite dimensions entails some nontrivial topological and functional analytic issues, making a deeper theoretical understanding indispensable toward applications. In this short work, we transfer the well-known property of compactness of the set of copulas in finite dimensions to the infinite-dimensional framework. As an application, we prove Sklar’s theorem in infinite dimensions via a topological argument and the notion of inverse systems.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"10 1","pages":"22 - 28"},"PeriodicalIF":0.7,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42452851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Polynomial bivariate copulas of degree five: characterization and some particular inequalities 五次多项式二元copula:表征及一些特殊不等式
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0101
A. Šeliga, Manuel Kauers, Susanne Saminger-Platz, R. Mesiar, A. Kolesárová, E. Klement
{"title":"Polynomial bivariate copulas of degree five: characterization and some particular inequalities","authors":"A. Šeliga, Manuel Kauers, Susanne Saminger-Platz, R. Mesiar, A. Kolesárová, E. Klement","doi":"10.1515/demo-2021-0101","DOIUrl":"https://doi.org/10.1515/demo-2021-0101","url":null,"abstract":"Abstract Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial copulas of degree 5 the values of several dependence parameters (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, and Gini’s gamma) lie in exactly the same intervals as for the Eyraud-Farlie-Gumbel-Morgenstern copulas. Finally we prove that these dependence parameters attain all possible values in ]−1, 1[ if polynomial copulas of arbitrary degree are considered.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"13 - 42"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2021-0101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48286157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors 齐次相关随机向量极值阶统计量的色散阶比较
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0118
M. Mesfioui, J. Trufin
{"title":"Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors","authors":"M. Mesfioui, J. Trufin","doi":"10.1515/demo-2021-0118","DOIUrl":"https://doi.org/10.1515/demo-2021-0118","url":null,"abstract":"Abstract In this paper, we investigate sufficient conditions for preservation property of the dispersive order for the smallest and largest order statistics of homogeneous dependent random vectors. Moreover, we establish sufficient conditions for ordering with the dispersive order the largest order statistics from dependent homogeneous samples of different sizes.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"385 - 393"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46859356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Sklar’s theorem, copula products, and ordering results in factor models 斯克拉定理，copula积，因子模型中的排序结果
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0113
Jonathan Ansari, L. Rüschendorf
{"title":"Sklar’s theorem, copula products, and ordering results in factor models","authors":"Jonathan Ansari, L. Rüschendorf","doi":"10.1515/demo-2021-0113","DOIUrl":"https://doi.org/10.1515/demo-2021-0113","url":null,"abstract":"Abstract We consider a completely specified factor model for a risk vector X = (X1, . . ., Xd), where the joint distributions of the components of X with a risk factor Z and the conditional distributions of X given Z are specified. We extend the notion of *-product of d-copulas as introduced for d = 2 and continuous factor distribution in Darsow et al. [6] and Durante et al. [8] to the multivariate and discontinuous case. We give a Sklar-type representation theorem for factor models showing that these *-products determine the copula of a completely specified factor model. We investigate in detail approximation, transformation, and ordering properties of *-products and, based on them, derive general orthant ordering results for completely specified factor models in dependence on their specifications. The paper generalizes previously known ordering results for the worst case partially specified risk factor models to some general classes of positive or negative dependent risk factor models. In particular, it develops some tools to derive sharp worst case dependence bounds in subclasses of completely specified factor models.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"267 - 306"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43524042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
On partially Schur-constant models and their associated copulas 部分schur -常数模型及其相关的copula
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0111
C. Lefèvre
{"title":"On partially Schur-constant models and their associated copulas","authors":"C. Lefèvre","doi":"10.1515/demo-2021-0111","DOIUrl":"https://doi.org/10.1515/demo-2021-0111","url":null,"abstract":"Abstract Schur-constant vectors are used to model duration phenomena in various areas of economics and statistics. They form a particular class of exchangeable vectors and, as such, rely on a strong property of symmetry. To broaden the field of applications, partially Schur-constant vectors are introduced which correspond to partially exchangeable vectors. First, their copulas of survival, said to be partially Archimedean, are explicitly obtained and analyzed. Next, much attention is devoted to the construction of different partially Schur-constant models with two groups of exchangeable variables. Finally, partial Schur-constancy is briefly extended to the modeling of nested and multi-level dependencies.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"225 - 242"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43485601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A tribute to Abe Sklar 向Abe Sklar致敬
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0110
C. Genest
{"title":"A tribute to Abe Sklar","authors":"C. Genest","doi":"10.1515/demo-2021-0110","DOIUrl":"https://doi.org/10.1515/demo-2021-0110","url":null,"abstract":"","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"200 - 224"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46493471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin 具有共同任意边界的三重独立随机变量的经典中心极限定理的反例
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0120
Guillaume Beaulieu, P. L. D. Micheaux, Frédéric Ouimet
{"title":"Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin","authors":"Guillaume Beaulieu, P. L. D. Micheaux, Frédéric Ouimet","doi":"10.1515/demo-2021-0120","DOIUrl":"https://doi.org/10.1515/demo-2021-0120","url":null,"abstract":"Abstract We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution F (satisfying very mild conditions). For two specific sequences, we obtain in closed form the asymptotic distribution of the sample mean. It is non-Gaussian (and depends on the specific choice of F). This allows us to illustrate the extent of the ‘failure’ of the classical central limit theorem (CLT) under triplewise independence. Our methodology is simple and can also be used to create, for any integer K, new K-tuplewise independent sequences that are not mutually independent. For K [four.tf], it appears that the sequences created using our methodology do verify a CLT, and we explain heuristically why this is the case.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"424 - 438"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43520946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Bernoulli process: simulation, estimation, and application 广义伯努利过程:模拟、估计及应用
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0106
Jeonghwa Lee
{"title":"Generalized Bernoulli process: simulation, estimation, and application","authors":"Jeonghwa Lee","doi":"10.1515/demo-2021-0106","DOIUrl":"https://doi.org/10.1515/demo-2021-0106","url":null,"abstract":"Abstract A generalized Bernoulli process (GBP) is a stationary process consisting of binary variables that can capture long-memory property. In this paper, we propose a simulation method for a sample path of GBP and an estimation method for the parameters in GBP. Method of moments estimation and maximum likelihood estimation are compared through empirical results from simulation. Application of GBP in earthquake data during the years of 1800-2020 in the region of conterminous U.S. is provided.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"141 - 155"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2021-0106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45863049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On a general class of gamma based copulas 一类基于γ的copula
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0117
B. Arnold, Matthew A. Arvanitis
{"title":"On a general class of gamma based copulas","authors":"B. Arnold, Matthew A. Arvanitis","doi":"10.1515/demo-2021-0117","DOIUrl":"https://doi.org/10.1515/demo-2021-0117","url":null,"abstract":"Abstract A large family of copulas with gamma components is examined, and interesting submodels are defined and analyzed. Parameter estimation is demonstrated for some of these submodels. A brief discussion of higher-dimensional versions is included.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"374 - 384"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48625232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Detecting departures from meta-ellipticity for multivariate stationary time series 多元平稳时间序列偏离元椭圆的检测
IF 0.7
Dependence Modeling Pub Date : 2021-01-01 DOI: 10.1515/demo-2021-0105
Axel Bücher, Miriam Jaser, A. Min
{"title":"Detecting departures from meta-ellipticity for multivariate stationary time series","authors":"Axel Bücher, Miriam Jaser, A. Min","doi":"10.1515/demo-2021-0105","DOIUrl":"https://doi.org/10.1515/demo-2021-0105","url":null,"abstract":"Abstract A test for detecting departures from meta-ellipticity for multivariate stationary time series is proposed. The large sample behavior of the test statistic is shown to depend in a complicated way on the underlying copula as well as on the serial dependence. Valid asymptotic critical values are obtained by a bootstrap device based on subsampling. The finite-sample performance of the test is investigated in a large-scale simulation study, and the theoretical results are illustrated by a case study involving financial log returns.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"9 1","pages":"121 - 140"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2021-0105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45154440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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