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## Análise de sensibilidade e resíduos em modelos de regressão com respostas bivariadas por meio de cópulas; Bivariate response regression models with copulas: Sensitivity and residual analysis

Gomes, Eduardo Monteiro de Castro
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Análise de dados com riscos semicompetitivos; Analysis of Semicompeting Risks Data

Patino, Elizabeth Gonzalez
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Teoria de valores extremos e copulas : distribuição valor extremo generalizada e copulas arquimedianas generalizadas trivariadas; Extreme value theory and copulas: generalized extreme value distribution and trivariate gneralized archimedean copulas

Marcio Luis Lanfredi Viola
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Teste grafico para o ajuste de copulas arquimedianas usando variaveis BIPIT : um estudo de simulação; Test chart for the adjustment Archimedean copulas using variables BIPIT : a study of simulation

Marta Cristina Colozza Bianchi
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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## Metodologia de avaliação econômica de projetos de petróleo com emprego de cópulas e processos estocásticos autorregressivos; Economic evaluation methodology of oil projects using copulas and stochastic autoregressive processes

João Bosco Dias Marques
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
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Esta tese, de caráter metodológico, é uma proposta de análise econômica de projetos de petróleo com emprego de cópulas e processos estocásticos autorregressivos envolvendo cinco variáveis fundamentais: o preço da commodity, a taxa mínima de atratividade (TMA), o custo de investimento (CAPEX), o custo operacional (OPEX) e a curva de produção de óleo. A premissa é a existência de uma estratégia de produção já estabelecida, de preferência decorrente de metodologias validadas em simulação numérica de reservatórios. O fluxo de caixa do projeto é baseado numa formulação simplificada de VPL e num modelo analítico de produção condicionado à referida estratégia. Para a aplicação desta metodologia são estimados modelos da família GARCH e ARMA para o preço do óleo e TMA, cópulas Arquimedianas para o CAPEX e o OPEX e cópulas elípticas para as variáveis que compõem a curva analítica de produção. Uma solução computacional, desenvolvida para a validação desta tese, possibilita não só a estimativa dos modelos como a incorporação destes no fluxo de caixa de um projeto de petróleo, tanto em regime de concessão como de partilha de produção. A matriz de incertezas combina os atributos preço e taxa para três cenários econômicos...

## Densités de copules archimédiennes hiérarchiques

Pham, David
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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Les copulas archimédiennes hiérarchiques ont récemment gagné en intérêt puisqu’elles généralisent la famille de copules archimédiennes, car elles introduisent une asymétrie partielle. Des algorithmes d’échantillonnages et des méthodes ont largement été développés pour de telles copules. Néanmoins, concernant l’estimation par maximum de vraisemblance et les tests d’adéquations, il est important d’avoir à disposition la densité de ces variables aléatoires. Ce travail remplie ce manque. Après une courte introduction aux copules et aux copules archimédiennes hiérarchiques, une équation générale sur les dérivées des noeuds et générateurs internes apparaissant dans la densité des copules archimédiennes hiérarchique. sera dérivée. Il en suit une formule tractable pour la densité des copules archimédiennes hiérarchiques. Des exemples incluant les familles archimédiennes usuelles ainsi que leur transformations sont présentés. De plus, une méthode numérique efficiente pour évaluer le logarithme des densités est présentée.; Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However...

## Conditional expectation formulae for copulas

Crane, G.; Van Der Hoek, J.
Fonte: Blackwell Publ Ltd Publicador: Blackwell Publ Ltd
Tipo: Artigo de Revista Científica
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Not only are copula functions joint distribution functions in their own right, they also provide a link between multivariate distributions and their lower-dimensional marginal distributions. Copulas have a structure that allows us to characterize all possible multivariate distributions, and therefore they have the potential to be a very useful statistical tool. Although copulas can be traced back to 1959, there is still much scope for new results, as most of the early work was theoretical rather than practical. We focus on simple practical tools based on conditional expectation, because such tools are not widely available. When dealing with data sets in which the dependence throughout the sample is variable, we suggest that copula-based regression curves may be more accurate predictors of specific outcomes than linear models. We derive simple conditional expectation formulae in terms of copulas and apply them to a combination of simulated and real data.; Glenis J. Crane and John van der Hoek; © 2008 Australian Statistical Publishing Association Inc.

## A flexible approach to multivariate risk modelling with a new class of copulas

Van Der Hoek, J.; Sherris, M.; Crane, G.
Fonte: Catholic University of Leuven; Leuven Publicador: Catholic University of Leuven; Leuven
Tipo: Conference paper
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We present a new class of copulas constructed using piece-wise linear distortions of some standard copulas. The method of construction of these copulas allows them to be readily calibrated by fitting to empirical multivariate risk data. We derive properties of this new class of copulas and present results from applying our distortions to a range of copulas including the Gaussian and Archimedean copulas. We consider tail dependence measures and show how distorted copulas can model various forms of tail dependence. The new form of distorted copula is convenient for numerical computation in insurance and financial risk modelling including risk measurement and management of portfolios. Gaussian copulas are often used in modelling credit risk portfolios and for many risk modelling applications in practice. We show how our approach can be applied to Gaussian copulas and derive properties of the distorted copulas. We illustrate the results by discussing the application of the approach to multivariate risk modelling in insurance and finance and compare the approach to other methods.; http://www.kuleuven.be/ime2006/abstract.php?id=22; John van der Hoek, Michael Sherris and Glenis Crane

## Copulas for Markovian dependence

Lagerås, Andreas N.
Tipo: Artigo de Revista Científica
Português
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Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some difficulties with using copulas even for Markov processes: some tractable copulas such as mixtures between copulas of complete co- and countermonotonicity and independence (Fr\'{e}chet copulas) are shown to imply quite a restricted type of Markov process and Archimedean copulas are shown to be incompatible with Markov chains. We also investigate Markov chains that are spreadable or, equivalently, conditionally i.i.d.; Comment: Published in at http://dx.doi.org/10.3150/09-BEJ214 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

## Nested Archimedean copulas: a new class of nonparametric tree structure estimators

Uyttendaele, Nathan
Tipo: Artigo de Revista Científica
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Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is built and second is collapsed if necessary to give an estimate of the target tree structure. Several examples of estimators from this class are given and the performance of each of these estimators, as well as of the only known comparable estimator, is assessed by means of a simulation study involving target structures in various dimensions, showing that the new estimators, besides being faster, usually offer better performance as well. Further, among the given examples of estimators from the new class, one of the best performing one is applied on three datasets: 482 students and their results to various examens, 26 European countries in 1979 and the percentage of workers employed in different economic activities, and 104 countries in 2002 for which various health-related variables are available. The resulting estimated trees offer valuable insights on the analyzed data. The future of nested Archimedean copulas in general is also discussed.

## Likelihood inference for Archimedean copulas

Hofert, Marius; Mächler, Martin; McNeil, Alexander J.
Tipo: Artigo de Revista Científica
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Explicit functional forms for the generator derivatives of well-known one-parameter Archimedean copulas are derived. These derivatives are essential for likelihood inference as they appear in the copula density, conditional distribution functions, or the Kendall distribution function. They are also required for several asymmetric extensions of Archimedean copulas such as Khoudraji-transformed Archimedean copulas. Access to the generator derivatives makes maximum-likelihood estimation for Archimedean copulas feasible in terms of both precision and run time, even in large dimensions. It is shown by simulation that the root mean squared error is decreasing in the dimension. This decrease is of the same order as the decrease in sample size. Furthermore, confidence intervals for the parameter vector are derived. Moreover, extensions to multi-parameter Archimedean families are given. All presented methods are implemented in the open-source R package nacopula and can thus easily be accessed and studied.; Comment: Part of this paper was presented at the copula workshop "Copula Models and Dependence" in Montreal (June 6 to June 9, 2011). The latest version of the R package nacopula can be downloaded from https://r-forge.r-project.org/projects/nacopula/

## Nonparametric estimation of the tree structure of a nested Archimedean copula

Segers, Johan; Uyttendaele, Nathan
Tipo: Artigo de Revista Científica
Português
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One of the features inherent in nested Archimedean copulas, also called hierarchical Archimedean copulas, is their rooted tree structure. A nonparametric, rank-based method to estimate this structure is presented. The idea is to represent the target structure as a set of trivariate structures, each of which can be estimated individually with ease. Indeed, for any three variables there are only four possible rooted tree structures and, based on a sample, a choice can be made by performing comparisons between the three bivariate margins of the empirical distribution of the three variables. The set of estimated trivariate structures can then be used to build an estimate of the target structure. The advantage of this estimation method is that it does not require any parametric assumptions concerning the generator functions at the nodes of the tree.; Comment: 25 pages, 9 figures

## Estimators for Archimedean copulas in high dimensions

Hofert, Marius; Maechler, Martin; McNeil, Alexander J.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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The performance of known and new parametric estimators for Archimedean copulas is investigated, with special focus on large dimensions and numerical difficulties. In particular, method-of-moments-like estimators based on pairwise Kendall's tau, a multivariate extension of Blomqvist's beta, minimum distance estimators, the maximum-likelihood estimator, a simulated maximum-likelihood estimator, and a maximum-likelihood estimator based on the copula diagonal are studied. Their performance is compared in a large-scale simulation study both under known and unknown margins (pseudo-observations), in small and high dimensions, under small and large dependencies, various different Archimedean families and sample sizes. High dimensions up to one hundred are considered for the first time and computational problems arising from such large dimensions are addressed in detail. All methods are implemented in the open source \R{} package \pkg{copula} and can thus be easily accessed and studied.

## Archimedean-based Marshall-Olkin Distributions and Related Copula Functions

Mulinacci, Sabrina
Tipo: Artigo de Revista Científica
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A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copulas and the Scale Mixture of Marshall-Olkin copulas (see Li, 2009),are obtained through suitable distortions of bivariate Archimedean copulas: this induces asymmetry, and the corresponding Kendall's tau as well as the tail dependence parameters are studied.

## Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions

McNeil, Alexander J.; Nešlehová, Johanna
Tipo: Artigo de Revista Científica
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It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a $d$-dimensional copula is that the generator is a $d$-monotone function. The class of $d$-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of $d$-dimensional $\ell_1$-norm symmetric distributions that place no point mass at the origin. The $d$-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math. J. 23 (1956) 189--207] in an analogous manner to the well-known Bernstein--Widder characterization of completely monotone generators in terms of the Laplace transform. These insights allow the construction of new Archimedean copula families and provide a general solution to the problem of sampling multivariate Archimedean copulas. They also yield useful expressions for the $d$-dimensional Kendall function and Kendall's rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for Archimedean copulas. The existence of a sharp lower bound for Archimedean copulas with respect to the positive lower orthant dependence ordering is shown.; Comment: Published in at http://dx.doi.org/10.1214/07-AOS556 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## Densities of nested Archimedean copulas

Hofert, Marius; Pham, David
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference it is important to have the density. The present work fills this gap. A general formula for the derivatives of the nodes and inner generators appearing in nested Archimedean copulas is developed. This leads to a tractable formula for the density of nested Archimedean copulas in arbitrary dimensions if the number of nesting levels is not too large. Various examples including famous Archimedean families and transformations of such are given. Furthermore, a numerically efficient way to evaluate the log-density is presented.; Comment: 25 pages

## Extending the Archimedean copula methodology to model multivariate survival data grouped in clusters of variable size

Prenen, Leen; Braekers, Roel; Duchateau, Luc
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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For the analysis of clustered survival data, two different types of models that take the association into account, are commonly used: frailty models and copula models. Frailty models assume that conditional on a frailty term for each cluster, the hazard functions of individuals within that cluster are independent. These unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster. Copula models on the other hand assume that the joint survival function of the individuals within a cluster is given by a copula function, evaluated in the marginal survival function of each individual. It is the copula function which describes the association between the lifetimes within a cluster. A major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal in order to set up manageable estimation procedures for the different model parameters. We describe in this manuscript a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of Archimedean copulas with completely monotone generator. We develop both one- and two-stage estimators for the different copula parameters. Furthermore we show the consistency and asymptotic normality of these estimators. Finally...

## Tails of multivariate Archimedean copulas

Charpentier, Arthur; Segers, Johan
Tipo: Artigo de Revista Científica
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A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails of the copula are classified into one of three classes each, one corresponding to asymptotic dependence and the other two to asymptotic independence. For a long list of single-parameter families, the relevant tail quantities are computed so that the corresponding classes in the decision tree can easily be determined. In addition, new models with tailor-made upper and lower tails can be constructed via a number of transformation methods. The frequently occurring category of asymptotic independence turns out to conceal a surprisingly rich variety of tail dependence structures.; Comment: to appear in the Journal of Multivariate Analysis

## Tail Properties of Multivariate Archimedean Copulas

Tipo: Artigo de Revista Científica
Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. A. J. McNeil and J. Ne\v{s}lehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate $\ell_1$-norm symmetric distributions. Building upon their results, we introduce a class of multivariate Markov processes that we call `Archimedean survival processes' (ASPs). An ASP is defined over a finite time interval, is equivalent in law to a multivariate gamma process, and its terminal value has an Archimedean survival copula. There exists a bijection from the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation.