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## Asymptotic properties of the Bernstein density copula for dependent data

Bouezmarni, Taoufik; Rombouts, Jeroen V. K.; Taamouti, Abderrahim
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
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Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α-mixing data using Bernstein polynomials. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality.

## U.S. subprime financial crisis contagion on BRIC and European Union stock markets

Bergmann,Daniel Reed; Securato,José Roberto; Savoia,José Roberto Ferreira; Contani,Eduardo Augusto do Rosário
Tipo: Artigo de Revista Científica Formato: text/html
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ABSTRACTThe Copula Theory was used to analyze contagion among the BRIC (Brazil, Russia, India and China) and European Union stock markets with the U.S. Equity Market. The market indexes used for the period between January 01, 2005 and February 27, 2010 are: MXBRIC (BRIC), MXEU (European Union) and MXUS (United States). This article evaluated the adequacy of the main copulas found in the financial literature using log-likelihood, Akaike information and Bayesian information criteria. This article provides a groundbreaking study in the area of contagion due to the use of conditional copulas, allowing to calculate the correlation increase between indexes with non-parametric approach. The conditional Symmetrized Joe-Clayton copula was the one that fitted better to the considered pairs of returns. Results indicate evidence of contagion effect in both markets, European Union and BRIC members, with a 5% significance level. Furthermore, there is also evidence that the contagion of U.S. financial crisis was more pronounced in the European Union than in the BRIC markets, with a 5% significance level. Therefore, stock portfolios formed by equities from the BRIC countries were able to offer greater protection during the subprime crisis. The results are aligned with recent papers that present an increase in correlation between stock markets...

## Les modèles vectoriels et multiplicatifs avec erreurs non-négatives de séries chronologiques.

Moutran, Emilie
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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L'objectif du présent mémoire vise à présenter des modèles de séries chronologiques multivariés impliquant des vecteurs aléatoires dont chaque composante est non-négative. Nous considérons les modèles vMEM (modèles vectoriels et multiplicatifs avec erreurs non-négatives) présentés par Cipollini, Engle et Gallo (2006) et Cipollini et Gallo (2010). Ces modèles représentent une généralisation au cas multivarié des modèles MEM introduits par Engle (2002). Ces modèles trouvent notamment des applications avec les séries chronologiques financières. Les modèles vMEM permettent de modéliser des séries chronologiques impliquant des volumes d'actif, des durées, des variances conditionnelles, pour ne citer que ces applications. Il est également possible de faire une modélisation conjointe et d'étudier les dynamiques présentes entre les séries chronologiques formant le système étudié. Afin de modéliser des séries chronologiques multivariées à composantes non-négatives, plusieurs spécifications du terme d'erreur vectoriel ont été proposées dans la littérature. Une première approche consiste à considérer l'utilisation de vecteurs aléatoires dont la distribution du terme d'erreur est telle que chaque composante est non-négative. Cependant...

## Defesa de territórios de acasalamento por machos da estaladeira-vermelha, Hamadryas amphinome (Lepidoptera: Nymphalidae), uma borboleta neotropical; Territorial defense of mating sites by males of the red cracker, Hamadryas amphinome (Lepidoptera: Nymphalidae), a neotropical butterfly

Victor Toni Lourenço
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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As borboletas do gênero Hamadryas são conhecidas há mais de 200 anos, mas até hoje intrigam os pesquisadores pela sua habilidade notável de produzir sons audíveis, em forma de estalos. Esse gênero neotropical ocorre tipicamente em clareiras e bordas de matas, onde são vistas em interações aéreas agressivas. Darwin sugeriu que tais interações estivessem diretamente relacionadas ao cortejo, mas hoje há especulações de que machos de várias espécies de Hamadryas defendem territórios de acasalamento, embora nenhum estudo decisivo tenha sido conduzido. Neste estudo, desenvolvido em uma floresta semidecídua no sudeste do Brasil, avaliamos e caracterizamos o comportamento territorial de Hamadryas amphinome (Linnaeus, 1767), também conhecida como estaladeira-vermelha. Usamos observações focais diárias intensivas para avaliar o comportamento, o padrão de atividade, o sucesso em disputas e a fidelidade territorial de borboletas previamente marcadas. Também procuramos compreender as regras usadas pelos machos para resolver disputas territoriais, como a influência da condição de residência, da idade e de possíveis fatores determinantes da capacidade de luta: comprimento alar e massa corporal. Os machos de H. amphinome defendem territórios de acasalamento no dossel de árvores emergentes localizadas próximas a clareiras e bordas de matas. Esses locais servem exclusivamente como `pontos de encontro' (landmark encounter sites)...

## Age and multiple mating effects on reproductive success of Grapholita molesta (Busck) (Lepidoptera, Tortricidae); Efeito da idade e de múltiplos acasalamentos no sucesso reprodutivo de Grapholita molesta (Busck) (Lepidoptera, Tortricidae

Morais, Rosana Matos de; Redaelli, Luiza Rodrigues; Sant'Ana, Josue
Tipo: Artigo de Revista Científica Formato: application/pdf
Português
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## Estimating Copula and Test of Independence based on a generalized framework of all rank-based Statistics in Bivariate Sample

Ghosh, Abhik; Chakravorty, Aritra
Tipo: Artigo de Revista Científica
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Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of formulating a multivariate distribution in such a way that various general types of dependence can be represented. In case of bivariate sample, the notion of estimating copula is closely related to that of testing independence in a bivariate sample, as when the components of the bivariate sample are independent the copula becomes simply product of two uniform distributions. So apart from non-parametric estimation of copulas we also considered it relevant to introduce some non-parametric tests to better understand the very essence of copula in the explanation of association between the components. In fact we will develop a general multivariate statistics that gives rise to a much larger class of non-parametric rank based statistics. This class of statistics can be used in estimation and testing for the association present in the bivariate sample. We choose some representative statistics from that class and compared their power in testing independence using simulation as an attempt to choose the best candidate in that class.; Comment: Project as a part of Multivariate Statistics Course in M. Stat. 1st year in Indian Statistical Institute...

## 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

## Flexible sampling of discrete data correlations without the marginal distributions

Kalaitzis, Alfredo; Silva, Ricardo
Tipo: Artigo de Revista Científica
Português
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Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity due to its modular parametrization of joint distributions. Among other properties, copulas provide a recipe for combining flexible models for univariate marginal distributions with parametric families suitable for potentially high dimensional dependence structures. More radically, the extended rank likelihood approach of Hoff (2007) bypasses learning marginal models completely when such information is ancillary to the learning task at hand as in, e.g., standard dimensionality reduction problems or copula parameter estimation. The main idea is to represent data by their observable rank statistics, ignoring any other information from the marginals. Inference is typically done in a Bayesian framework with Gaussian copulas, and it is complicated by the fact this implies sampling within a space where the number of constraints increases quadratically with the number of data points. The result is slow mixing when using off-the-shelf Gibbs sampling. We present an efficient algorithm based on recent advances on constrained Hamiltonian Markov chain Monte Carlo that is simple to implement and does not require paying for a quadratic cost in sample size.; Comment: An overhauled version of the experimental section moved to the main paper. Old experimental section moved to supplementary material

## Copula-type Estimators for Flexible Multivariate Density Modeling using Mixtures

Tran, Minh-Ngoc; Giordani, Paolo; Mun, Xiuyan; Kohn, Robert; Pitt, Mike
Tipo: Artigo de Revista Científica
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Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the marginals of the joint dependence structure is known. This can only be done for a restricted set of copulas, e.g. a normal copula. Our article introduces copula-type estimators for flexible multivariate density estimation which also allow the marginal densities to be modeled separately from the joint dependence, as in copula modeling, but overcomes the lack of flexibility of most popular copula estimators. An iterative scheme is proposed for estimating copula-type estimators and its usefulness is demonstrated through simulation and real examples. The joint dependence is is modeled by mixture of normals and mixture of normals factor analyzers models, and mixture of t and mixture of t factor analyzers models. We develop efficient Variational Bayes algorithms for fitting these in which model selection is performed automatically. Based on these mixture models, we construct four classes of copula-type densities which are far more flexible than current popular copula densities, and outperform them in simulation and several real data sets.; Comment: 27 pages...

## Spatial composite likelihood inference using local C-vines

Erhardt, Tobias Michael; Czado, Claudia; Schepsmeier, Ulf
Tipo: Artigo de Revista Científica
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We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. This approach combines established methods to model (spatial) dependencies. On the one hand the geostatistical concept utilizing spatial differences between the variable locations to model the extend of spatial dependencies is applied. On the other hand the flexible class of C-vine copulas is utilized to model the spatial dependency structure locally. These local C-vine copulas are parametrized jointly, exploiting an existing relationship between the copula parameters and the respective spatial distances and elevation differences, and are combined in a composite likelihood approach. The new methodology called spatial local C-vine composite likelihood (S-LCVCL) method benefits from the fact that it is able to capture non-Gaussian dependency structures. The development and validation of the new methodology is illustrated using a data set of daily mean temperatures observed at 73 observation stations spread over Germany. For validation continuous ranked probability scores are utilized. Comparison with two other approaches of spatial dependency modeling introduced in yet unpublished work of Erhardt...

## Asymptotics of empirical copula processes under non-restrictive smoothness assumptions

Segers, Johan
Tipo: Artigo de Revista Científica
Português
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Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is non-restrictive in the sense that it is needed anyway to ensure that the candidate limiting process exists and has continuous trajectories. In addition, resampling methods based on the multiplier central limit theorem, which require consistent estimation of the first-order derivatives, continue to be valid. Under certain growth conditions on the second-order partial derivatives that allow for explosive behavior near the boundaries, the almost sure rate in Stute's representation of the empirical copula process can be recovered. The conditions are verified, for instance, in the case of the Gaussian copula with full-rank correlation matrix, many Archimedean copulas, and many extreme-value copulas.; Comment: Published in at http://dx.doi.org/10.3150/11-BEJ387 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

## Using the Notion of Copula in Tomography

Pougaza, Doriano-Boris; Mohammad-Djafari, A.; Bercher, Jean-François
Tipo: Artigo de Revista Científica
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In 1917 Johann Radon introduced the Radon transform which is used in 1963 by A. M. Cormack for application in the context of tomographic image reconstruction. He proposed to reconstruct the spatial variation of the material density of the body from X-Ray images (radiographies) for different directions. Independently G. N. Hounsfield derived an algorithm and built the first medical CT scanner. Basically the idea of the X-ray CT is to get an image of the interior structure of an object by X-raying the object from many different directions. The mathematical problem is then estimating a multivariate function from its line integrals. Four year before Cormack's idea, Abe Sklar introduced a theory in the context of Statistics called copula. Shortly copulas are functions that link multivariate distributions to theirs univariate marginal functions. It appeared that copulas captivated all dependence structure concerning the marginal functions and offer a wide range of parametric family model which could be used as a model for the joint distribution function. This statistical problem is the same as in Tomography, because a marginal density is obtained from a line integral of its joint distribution. In the particular case of only given horizontal and vertical projections corresponding to a given two marginal functions...

## Paths and indices of maximal tail dependence

Furman, Edward; Su, Jianxi; Zitikis, Ričardas
Tipo: Artigo de Revista Científica
Português
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We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so.

## Perturbed Copula: Introducing the skew effect in the co-dependence

Elices, Alberto; Fouque, Jean-Pierre
Tipo: Artigo de Revista Científica
Português
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Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of this copula is derived through an asymptotic expansion under the assumption of a common fast mean reverting stochastic volatility factor. This paper applies this new perturbed copula to the valuation of derivative products; in particular FX quanto options to a third currency. A calibration procedure to fit the skew of both underlying securities is presented. The action of the perturbed copula is interpreted compared to the Gaussian copula. A real worked example is carried out comparing both copulas and a local volatility model with constant correlation for varying maturities, correlations and skew configurations.; Comment: 34 pages, 6 figures and 3 tables

## Remarks on the speed of convergence of mixing coefficients and applications

Longla, Martial
Tipo: Artigo de Revista Científica
Português
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In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the Metropolis-hastings algorithm and give conditions on the proposal that ensure exponential $\rho$-mixing, $\beta$-mixing and $\phi$-mixing. A general necessary condition on symmetric copulas to generate exponential $\rho$-mixing or $\phi$-mixing is given. At the end of the paper, we comment and improve some of our previous results on mixtures of copulas.; Comment: arXiv admin note: text overlap with arXiv:1207.5762

## COPAR - Multivariate time series modeling using the COPula AutoRegressive model

Tipo: Artigo de Revista Científica
Português
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Analysis of multivariate time series is a common problem in areas like finance and economics. The classical tool for this purpose are vector autoregressive models. These however are limited to the modeling of linear and symmetric dependence. We propose a novel copula-based model which allows for non-linear and asymmetric modeling of serial as well as between-series dependencies. The model exploits the flexibility of vine copulas which are built up by bivariate copulas only. We describe statistical inference techniques for the new model and demonstrate its usefulness in three relevant applications: We analyze time series of macroeconomic indicators, of electricity load demands and of bond portfolio returns.; Comment: arXiv admin note: extreme overlap with arXiv:1202.1998

## Copula variational inference

Tran, Dustin; Blei, David M.; Airoldi, Edoardo M.
Tipo: Artigo de Revista Científica
Português
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We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-field or structured approach. Copula variational inference has many advantages: it reduces bias; it is less sensitive to local optima; it is less sensitive to hyperparameters; and it helps characterize and interpret the dependency among the latent variables.; Comment: Appears in Neural Information Processing Systems, 2015

## A New Class of Nonsymmetric Multivariate Dependence Measures

Li, Hui
Tipo: Artigo de Revista Científica
Português
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Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one random variable on a group of random variables. The measures are nonparametric in that they are copula-based and are invariant under continuous bijective transformations on the group of random variables. We also construct explicitly new measures that satisfy the conditions. Besides, we extend the star product on bivariate copulas to multivariate copulas and prove the DPI condition and self-equitability for the new measures. A further extension to measures of dependence of one group of random variables on another group of random variables is also discussed.; Comment: 20 pages

## Estimation of Extreme Quantiles for Functions of Dependent Random Variables

Gong, Jinguo; Li, Yadong; Peng, Liang; Yao, Qiwei
Tipo: Artigo de Revista Científica