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Article: Grouped normal variance mixtures
Title | Grouped normal variance mixtures |
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Authors | |
Keywords | Copulas Densities Distribution functions Grouped normal variance mixtures Grouped t copula Quasi-random number sequences Risk measures |
Issue Date | 2020 |
Citation | Risks, 2020, v. 8, n. 4, article no. 103 How to Cite? |
Abstract | Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors where components within a group are of similar type, but where different groups have components of quite different type. This paper provides an encompassing body of algorithms to address the computational challenges when working with this class of distributions. In particular, the distribution function and copula are estimated efficiently using randomized quasi-Monte Carlo (RQMC) algorithms. We propose to estimate the log-density function, which is in general not available in closed form, using an adaptive RQMC scheme. This, in turn, gives rise to a likelihood-based fitting procedure to jointly estimate the parameters of a grouped normal mixture copula jointly. We also provide mathematical expressions and methods to compute Kendall’s tau, Spearman’s rho and the tail dependence coefficient λ. All algorithms presented are available in the R package nvmix (version ≥ 0.0.5). |
Persistent Identifier | http://hdl.handle.net/10722/325490 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hintz, Erik | - |
dc.contributor.author | Hofert, Marius | - |
dc.contributor.author | Lemieux, Christiane | - |
dc.date.accessioned | 2023-02-27T07:33:43Z | - |
dc.date.available | 2023-02-27T07:33:43Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Risks, 2020, v. 8, n. 4, article no. 103 | - |
dc.identifier.uri | http://hdl.handle.net/10722/325490 | - |
dc.description.abstract | Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors where components within a group are of similar type, but where different groups have components of quite different type. This paper provides an encompassing body of algorithms to address the computational challenges when working with this class of distributions. In particular, the distribution function and copula are estimated efficiently using randomized quasi-Monte Carlo (RQMC) algorithms. We propose to estimate the log-density function, which is in general not available in closed form, using an adaptive RQMC scheme. This, in turn, gives rise to a likelihood-based fitting procedure to jointly estimate the parameters of a grouped normal mixture copula jointly. We also provide mathematical expressions and methods to compute Kendall’s tau, Spearman’s rho and the tail dependence coefficient λ. All algorithms presented are available in the R package nvmix (version ≥ 0.0.5). | - |
dc.language | eng | - |
dc.relation.ispartof | Risks | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Copulas | - |
dc.subject | Densities | - |
dc.subject | Distribution functions | - |
dc.subject | Grouped normal variance mixtures | - |
dc.subject | Grouped t copula | - |
dc.subject | Quasi-random number sequences | - |
dc.subject | Risk measures | - |
dc.title | Grouped normal variance mixtures | - |
dc.type | Article | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.3390/risks8040103 | - |
dc.identifier.scopus | eid_2-s2.0-85092394139 | - |
dc.identifier.volume | 8 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | article no. 103 | - |
dc.identifier.epage | article no. 103 | - |
dc.identifier.eissn | 2227-9091 | - |
dc.identifier.isi | WOS:000601648700001 | - |