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2001): “Clarify: Software for Interpreting and Presenting Statistical Results
 Journal of Statistical Software
"... and distribute this program provided that no charge is made and the copy is identical to the original. To request an exception, please contact Michael Tomz. Contents 1 ..."
Abstract

Cited by 294 (2 self)
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and distribute this program provided that no charge is made and the copy is identical to the original. To request an exception, please contact Michael Tomz. Contents 1
Understanding relationships using copulas
 North American Actuarial Journal
, 1998
"... This article introduces actuaries to the concept of "copulas, " a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of prob ..."
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Cited by 217 (8 self)
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This article introduces actuaries to the concept of &quot;copulas, &quot; a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic metric spaces. Recently, there has been a rapidly developing literature on the statistical properties and applications of copulas. This article explores some of these practical applications, including estimation of joint life mortality and multidecrement models. In addition, we describe basic properties of copulas, their relationships to measures of dependence and several families of copulas that have appeared in the literature. An annotated bibliography provides a resource for researchers and practitioners who wish to continue their study of copulas. This article will also be useful to those who wish to use copulas for statistical inference. Statistical inference procedures are illustrated using insurance company data on losses and expenses. For this data, we (1) show how to fit copulas and (2) describe their usefulness by pricing a reinsurance contract and estimating expenses for prespecified losses.
An exact likelihood analysis of the multinomial probit model
, 1994
"... We develop new methods for conducting a finite sample, likelihoodbased analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evalu ..."
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Cited by 163 (6 self)
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We develop new methods for conducting a finite sample, likelihoodbased analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches. Both simulated and actual consumer panel data are used to fit sixdimensional choice models. We also develop methods for analyzing random coefficient and multiperiod probit models.
Estimation of copulabased semiparametric time series models
 J. Econometrics
, 2006
"... This paper studies the estimation of a class of copulabased semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition di ..."
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Cited by 84 (11 self)
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This paper studies the estimation of a class of copulabased semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric. Models in this class are easy to simulate, and can be expressed as semiparametric regression transformation models. One advantage of this copula approach is to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tailedness) of a time series. We present conditions under which processes generated by models in this class are βmixing; naturally, these conditions depend only on the copula specification. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. Estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles are easily obtained from estimators of the marginal distribution and the copula parameter; their √ n − consistency and asymptotic normality can be obtained using the Delta method. In addition, the semiparametric
Methods for the Computation of Multivariate tProbabilities
 Computing Sciences and Statistics
, 2000
"... This paper compares methods for the numerical computation of multivariate tprobabilities for hyperrectangular integration regions. Methods based on acceptancerejection, sphericalradial transformations and separationofvariables transformations are considered. Tests using randomly chosen problems ..."
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Cited by 83 (11 self)
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This paper compares methods for the numerical computation of multivariate tprobabilities for hyperrectangular integration regions. Methods based on acceptancerejection, sphericalradial transformations and separationofvariables transformations are considered. Tests using randomly chosen problems show that the most efficient numerical methods use a transformation developed by Genz (1992) for multivariate normal probabilities. These methods allow moderately accurate multivariate tprobabilities to be quickly computed for problems with as many as twenty variables. Methods for the noncentral multivariate tdistribution are also described. Key Words: multivariate tdistribution, noncentral distribution, numerical integration, statistical computation. 1 Introduction A common problem in many statistics applications is the numerical computation of the multivariate t (MVT) distribution function (see Tong, 1990) defined by T(a; b; \Sigma; ) = \Gamma( +m 2 ) \Gamma( 2 ) p j\Sigma...
2002): "A New Class of Multivariate Skew Densities, with Application to GARCH Models," working paper
"... We propose a practical and flexible solution to introduce skewness in multivariate symmetrical distributions. Applying this procedure to the multivariate Student density leads to a “multivariate skewStudent ” density, for which each marginal has a different asymmetry coefficient. Combined with a m ..."
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Cited by 76 (6 self)
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We propose a practical and flexible solution to introduce skewness in multivariate symmetrical distributions. Applying this procedure to the multivariate Student density leads to a “multivariate skewStudent ” density, for which each marginal has a different asymmetry coefficient. Combined with a multivariate GARCH model, this new family of distributions is potentially useful for modelling stock returns, which are known to be conditionally heteroskedastic, fattailed, and often skew. In an application to the daily returns of the NASDAQ and the DAX, it is found that this density suits well the data and clearly outperforms its symmetric competitor.
Modeling and Generating Random Vectors with Arbitrary Marginal Distributions and Correlation Matrix
, 1997
"... We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random ..."
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Cited by 70 (4 self)
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We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random vector into the desired random vector, so we refer to these vectors as having a NORTA (NORmal To Anything) distribution. NORTA vectors are most useful when the marginal distributions of the component random variables are neither identical nor from the same family of distributions, and they are particularly valuable when the dimension of the random vector is greater than two. Several numerical examples are provided. Keywords: simulation, random vector, input modeling, correlation matrix, copulas 1 Introduction In many stochastic simulations, simple input modelsidependent and identically distributed sequences from standard probability distributionsare not faithful representations of th...
The Polarimetric G Distribution for SAR Data Analysis
, 2003
"... Remote sensing data, and radar data in particular, have become an essential tool for enviromental studies. Many airborne polarimetric sensors are currently operational, and many more will be available in the near future including spaceborne platforms. The signaltonoise ratio of this kind of imager ..."
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Cited by 46 (7 self)
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Remote sensing data, and radar data in particular, have become an essential tool for enviromental studies. Many airborne polarimetric sensors are currently operational, and many more will be available in the near future including spaceborne platforms. The signaltonoise ratio of this kind of imagery is lower than that of optical information requiring, thus, a careful statistical modelling. This modelling may lead to useful or useless techniques for image processing and analysis, according to the agreement between the data and their assumed properties. Several distributions have been used to describe Synthetic Aperture Radar (SAR) data. Many of these univaritate laws arise by assuming the multiplicative model, such as Rayleigh, Square Root of Gamma, Exponential, Gamma, and the class of the I distributions. The adequacy of these distributions depends on the detection (amplitude, intensity, complex etc.), the number of looks, and the homogeneity of the data. In Frery, Muller, Yanasse and Sant'Anna (1997) another class of univariate distributions, called G, was proposed to model extremely heterogeneous clutter, such as urban areas, as well as other types of clutter. This paper extends the univariate family to the multivariate multilook polarimetric situation: the P law. The new family has the classical polarimetric multilook P distribution as a particular case, but another special case is shown more flexible and tractable, while having the same number of parameters and fully retaining their interpretability: the P law. The main properties of this new multivariate distribution are shown. Some results of modelling polarimetric data using P distribution are presented for two airborne polarimetric systems and a variety of targets, showing its expresiveness b...
BROWNIAN DISTANCE COVARIANCE
"... Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to productmoment covariance and correlation, but generalize and extend these classica ..."
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Cited by 34 (1 self)
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Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to productmoment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, both can be called Brownian distance covariance. In the bivariate case, Brownian covariance is the natural extension of productmoment covariance, as we obtain Pearson productmoment covariance by replacing the Brownian motion in the definition with identity. The corresponding statistic has an elegantly simple computing formula. Advantages of applying Brownian covariance and correlation vs the classical Pearson covariance and correlation are discussed and illustrated. 1. Introduction. The