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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2014
Português

Relevância na Pesquisa

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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.

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## Multivariate Spearman's rho for aggregating ranks using copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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We study the problem of rank aggregation: given a set of ranked lists, we
want to form a consensus ranking. Furthermore, we consider the case of extreme
lists: i.e., only the rank of the best or worst elements are known. We impute
missing ranks by the average value and generalise Spearman's \rho to extreme
ranks. Our main contribution is the derivation of a non-parametric estimator
for rank aggregation based on multivariate extensions of Spearman's \rho, which
measures correlation between a set of ranked lists. Multivariate Spearman's
\rho is defined using copulas, and we show that the geometric mean of
normalised ranks maximises multivariate correlation. Motivated by this, we
propose a weighted geometric mean approach for learning to rank which has a
closed form least squares solution. When only the best or worst elements of a
ranked list are known, we impute the missing ranks by the average value,
allowing us to apply Spearman's \rho. Finally, we demonstrate good performance
on the rank aggregation benchmarks MQ2007 and MQ2008.

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## A goodness-of-fit test for bivariate extreme-value copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/02/2011
Português

Relevância na Pesquisa

26.95%

It is often reasonable to assume that the dependence structure of a bivariate
continuous distribution belongs to the class of extreme-value copulas. The
latter are characterized by their Pickands dependence function. In this paper,
a procedure is proposed for testing whether this function belongs to a given
parametric family. The test is based on a Cram\'{e}r--von Mises statistic
measuring the distance between an estimate of the parametric Pickands
dependence function and either one of two nonparametric estimators thereof
studied by Genest and Segers [Ann. Statist. 37 (2009) 2990--3022]. As the
limiting distribution of the test statistic depends on unknown parameters, it
must be estimated via a parametric bootstrap procedure, the validity of which
is established. Monte Carlo simulations are used to assess the power of the
test and an extension to dependence structures that are left-tail decreasing in
both variables is considered.; Comment: Published in at http://dx.doi.org/10.3150/10-BEJ279 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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## Generation of degree-correlated networks using copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

#Physics - Data Analysis, Statistics and Probability#Computer Science - Social and Information Networks#Mathematical Physics#Physics - Physics and Society

Dynamical processes on complex networks such as information propagation,
innovation diffusion, cascading failures or epidemic spreading are highly
affected by their underlying topologies as characterized by, for instance,
degree-degree correlations. Here, we introduce the concept of copulas in order
to artificially generate random networks with an arbitrary degree distribution
and a rich a priori degree-degree correlation (or `association') structure. The
accuracy of the proposed formalism and corresponding algorithm is numerically
confirmed. The derived network ensembles can be systematically deployed as
proper null models, in order to unfold the complex interplay between the
topology of real networks and the dynamics on top of them.

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## Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

We study the adaptive estimation of copula correlation matrix $\Sigma$ for
elliptical copulas. In this context, the correlations are connected to
Kendall's tau through a sine function transformation. Hence, a natural estimate
for $\Sigma$ is the plug-in estimator $\widehat\Sigma$ with Kendall's tau
statistic. We first obtain a sharp bound for the operator norm of $\widehat
\Sigma - \Sigma$. Then, we study a factor model for $\Sigma$, for which we
propose a refined estimator $\widetilde\Sigma$ by fitting a low-rank matrix
plus a diagonal matrix to $\widehat\Sigma$ using least squares with a nuclear
norm penalty on the low-rank matrix. The bound for the operator norm of
$\widehat \Sigma - \Sigma$ serves to scale the penalty term, and we obtain
finite sample oracle inequalities for $\widetilde\Sigma$. We also consider an
elementary factor model of $\Sigma$, for which we propose closed-form
estimators. We provide data-driven versions for all our estimation procedures
and performance bounds.

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## Estimators for Archimedean copulas in high dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Statistics - Computation#Mathematics - Numerical Analysis#Statistics - Other Statistics#62H12, 62F10, 62H99, 62H20, 65C60

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.

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## A new bivariate extension of FGM copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/03/2011
Português

Relevância na Pesquisa

26.95%

We propose a new family of copulas generalizing the
Farlie-Gumbel-Morgenstern family and generated by two univariate functions.
The main feature of this family is to permit the modeling of high positive
dependence. In particular, it is established that the range of the Spearman's
Rho is [-3/4,1] and that the upper tail dependence coefficient can reach any
value in [0,1]. Necessary and sufficient conditions are given on the generating
functions in order to obtain various dependence properties. Some examples of
parametric subfamilies are provided.

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## Model-based clustering of Gaussian copulas for mixed data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

Clustering task of mixed data is a challenging problem. In a probabilistic
framework, the main difficulty is due to a shortage of conventional
distributions for such data. In this paper, we propose to achieve the mixed
data clustering with a Gaussian copula mixture model, since copulas, and in
particular the Gaussian ones, are powerful tools for easily modelling the
distribution of multivariate variables. Indeed, considering a mixing of
continuous, integer and ordinal variables (thus all having a cumulative
distribution function), this copula mixture model defines intra-component
dependencies similar to a Gaussian mixture, so with classical correlation
meaning. Simultaneously, it preserves standard margins associated to
continuous, integer and ordered features, namely the Gaussian, the Poisson and
the ordered multinomial distributions. As an interesting by-product, the
proposed mixture model generalizes many well-known ones and also provides tools
of visualization based on the parameters. At a practical level, the Bayesian
inference is retained and it is achieved with a Metropolis-within-Gibbs
sampler. Experiments on simulated and real data sets finally illustrate the
expected advantages of the proposed model for mixed data: flexible and
meaningful parametrization combined with visualization features.

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## Shaping tail dependencies by nesting box copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

We introduce a family of copulas which are locally piecewise uniform in the
interior of the unit cube of any given dimension. Within that family, the
simultaneous control of tail dependencies of all projections to faces of the
cube is possible and we give an efficient sampling algorithm. The combination
of these two properties may be appealing to risk modellers.; Comment: 25 pages, 3 figures, added reference, remarks in Section 6, corrected
typos

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## Additive Models for Conditional Copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/07/2014
Português

Relevância na Pesquisa

26.95%

Conditional copulas are flexible statistical tools that couple joint
conditional and marginal conditional distributions. In a linear regression
setting with more than one covariate and two dependent outcomes, we propose the
use of additive models for conditional bivariate copula models and discuss
computation and model selection tools for performing Bayesian inference. The
method is illustrated using simulations and a real example.

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## Time and Space Varying Copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/12/2008
Português

Relevância na Pesquisa

26.95%

In this article we review existing literature on dynamic copulas and then
propose an n-copula which varies in time and space. Our approach makes use of
stochastic differential equations, and gives rise to a dynamic copula which is
able to capture the dependence between multiple Markov diffusion processes.
This model is suitable for pricing basket derivatives in finance and may also
be applicable to other areas such as bioinformatics and environmental science.

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## Computation of copulas by Fourier methods

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

We provide an integral representation for the (implied) copulas of dependent
random variables in terms of their moment generating functions. The proof uses
ideas from Fourier methods for option pricing. This representation can be used
for a large class of models from mathematical finance, including L\'evy and
affine processes. As an application, we compute the implied copula of the NIG
L\'evy process which exhibits notable time-dependence.; Comment: 7 pages, 3 figures

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## Copulas in three dimensions with prescribed correlations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/04/2010
Português

Relevância na Pesquisa

26.95%

Given an arbitrary three-dimensional correlation matrix, we prove that there
exists a three-dimensional joint distribution for the random variable $(X,Y,Z)$
such that $X$,$Y$ and $Z$ are identically distributed with beta distribution
$\beta_{k,k}(dx)$ on $(0,1)$ if $k\geq 1/2$. This implies that any correlation
structure can be attained for three-dimensional copulas.; Comment: 15 pages, 2 figures

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## Using a priori knowledge to construct copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/04/2010
Português

Relevância na Pesquisa

26.95%

Our purpose is to model the dependence between two random variables, taking
into account a priori knowledge on these variables. For example, in many
applications (oceanography, finance...), there exists an order relation between
the two variables; when one takes high values, the other cannot take low
values, but the contrary is possible. The dependence for the high values of the
two variables is, therefore, not symmetric.
However a minimal dependence also exists: low values of one variable are
associated with low values of the other variable. The dependence can also be
extreme for the maxima or the minima of the two variables. In this paper, we
construct step by step asymmetric copulas with asymptotic minimal dependence,
and with or without asymptotic maximal dependence, using mixture variables to
get at first asymmetric dependence and then minimal dependence. We fit these
models to a real dataset of sea states and compare them using Likelihood Ratio
Tests when they are nested, and BIC- criterion (Bayesian Information criterion)
otherwise.

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## Semi-Supervised Domain Adaptation with Non-Parametric Copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/01/2013
Português

Relevância na Pesquisa

26.95%

A new framework based on the theory of copulas is proposed to address semi-
supervised domain adaptation problems. The presented method factorizes any
multivariate density into a product of marginal distributions and bivariate
cop- ula functions. Therefore, changes in each of these factors can be detected
and corrected to adapt a density model accross different learning domains.
Impor- tantly, we introduce a novel vine copula model, which allows for this
factorization in a non-parametric manner. Experimental results on regression
problems with real-world data illustrate the efficacy of the proposed approach
when compared to state-of-the-art techniques.; Comment: 9 pages, Appearing on Advances in Neural Information Processing
Systems 25

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## Modeling covariate-contingent correlation and tail-dependence with copulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/12/2013
Português

Relevância na Pesquisa

26.95%

Copulas provide an attractive approach for constructing multivariate
densities with flexible marginal distributions and different forms of
dependence. Of particular importance in many areas is the possibility of
explicitly modeling tail-dependence. Most of the available approaches estimate
tail-dependence and correlations via nuisance parameters, yielding results that
are neither tractable nor interpretable for practitioners. We propose a general
Bayesian approach for directly modeling tail-dependence and correlations as
explicit functions of covariates. Our method allows for variable selection
among the covariates in the marginal models and in the copula parameters.
Posterior inference is carried out using a novel and efficient MCMC simulation
method.

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## On mixtures of copulas and mixing coefficients

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.95%

We show that if the density of the absolutely continuous part of a copula is
bounded away from zero on a set of Lebesgue measure 1, then that copula
generates \textquotedblleft lower $\psi$-mixing\textquotedblright\ stationary
Markov chains. This conclusion implies $\phi$-mixing, $\rho$-mixing,
$\beta$-mixing and \textquotedblleft interlaced $\rho$-mixing\textquotedblright
. We also provide some new results on the mixing structure of Markov chains
generated by mixtures of copulas.; Comment: 11pages

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## Gaussian Process Conditional Copulas with Applications to Financial Time Series

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2013
Português

Relevância na Pesquisa

26.95%

The estimation of dependencies between multiple variables is a central
problem in the analysis of financial time series. A common approach is to
express these dependencies in terms of a copula function. Typically the copula
function is assumed to be constant but this may be inaccurate when there are
covariates that could have a large influence on the dependence structure of the
data. To account for this, a Bayesian framework for the estimation of
conditional copulas is proposed. In this framework the parameters of a copula
are non-linearly related to some arbitrary conditioning variables. We evaluate
the ability of our method to predict time-varying dependencies on several
equities and currencies and observe consistent performance gains compared to
static copula models and other time-varying copula methods.

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## When does the stock market listen to economic news? New evidence from copulas and news wires

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/10/2014
Português

Relevância na Pesquisa

26.95%

We study association between macroeconomic news and stock market returns
using the statistical theory of copulas, and a new comprehensive measure of
news based on the indexing of news wires. We find the impact of economic news
on equity returns to be nonlinear and asymmetric. In particular, controlling
for economic conditions and surprises associated with releases of economic
data, we find that the market reacts strongly and negatively to the most
unfavourable macroeconomic news, but appears to largely discount the good news.
This relationship persists throughout the different stages of the business
cycle.; Comment: 37 pages, 5 figures

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## On the identifiability of copulas in bivariate competing risks models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2013
Português

Relevância na Pesquisa

26.95%

In competing risks models, the joint distribution of the event times is not
identifiable even when the margins are fully known, which has been referred to
as the "identifiability crisis in competing risks analysis" (Crowder, 1991). We
model the dependence between the event times by an unknown copula and show that
identification is actually possible within many frequently used families of
copulas. The result is then extended to the case where one margin is unknown.; Comment: 16 pages, 3 figures

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