An Introduction to Copulas (Springer Series in Statistics)

By Roger B. Nelsen. 2006

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The Variational Gaussian Process (2015, background): “It places a continuous Bayesian nonparametric prior over mean-ﬁeld parameters.”
Hierarchical Variational Models (2015, methodology): “For example, copulas explicitly introduce dependence among d random variables by using joint distributions on d -dimensional hypercubes (Nelsen, 2006).”
Learning Connections in Financial Time Series (2013, methodology): “Using this metric, our approach consistently outperforms the most popular techniques in the financial literature, e.g., t-copula (Nelsen, 2006).”
Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond (2009, background): “The Annals of Applied Probability 2009, Vol. 19, No. 6, 2362–2405 DOI: 10.1214/08-AAP548 © Institute of Mathematical Statistics, 2009”
Handling Endogenous Regressors by Joint Estimation Using Copulas (2012, unknown): “In the statistics literature, various copula functions have been studied (see Nelsen 2006 or Balakrishnan and Lai 2009).”
Uncertainty analysis of bias from satellite rainfall estimates using copula method (2014, background): “The n-dimensional multivariate Gaussian copula is derived from the multivariate normal distribution (Nelsen, 2006) and described with a correlation matrix ρn × n (n is the number of variables) as follows: Cnρ u1;…;unð Þ ¼ Fnρ F−1 u1ð Þ;…; F−1 unð Þ h i ð8Þ Where ui is the ith random vector and Fρn…”
Distorted Copulas: Constructions and Tail Dependence (2010, methodology): “Communications in Statistics—Theory and Methods, 39: 2288–2301, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 0361-0926 print/1532-415X online DOI: 10.1080/03610920903039506 Distorted Copulas: Constructions and Tail Dependence FABRIZIO DURANTE1, RACHELE FOSCHI2, AND PETER SARKOCI1 1Department o”
Probability Distributions as Program Variables (2009, background): “Approximation with Mixture Models: It has been already reported that for certain kinds of distributions the results of binary operations can”
Sequential Monte Carlo on large binary sampling spaces (2011, methodology): “There have been earlier attempts to sample binary vectors via copulae: Lee (1993) describes how to construct an Archimedean copula, more precisely the Frank family (Nelsen, 2006, p.119), for sampling multivariate binary data.”
An empirical analysis of multivariate copula models (2009, background): “…and convex function with ’(1)¼ 0, ’(0) 1 and let ’[ 1] be the so-called pseudo-inverse of ’ defined by ’½ 1 ðtÞ ’ 1ðtÞ 0 t ’ð0Þ; 0 ’ð0Þ t 1: It can be shown (see, e.g. Nelsen, 2006) that Cðu1; u2Þ ¼ ’½ 1 ’ðu1Þ þ ’ðu2Þ defines a class of bivariate copulas, the so-called Archimedean copulas.”