On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables

Fredricks, Gregory A.; Nelsen, Roger B.

doi:10.1016/j.jspi.2006.06.045

Cited by 170 publications

(109 citation statements)

References 11 publications

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“…7 are the elliptical and the Archimedian copulas family as given below. Details about other copula families and their selection can be found in ; Embrechts et al (2001); Chen and Fan (2005); Frees and Valdez (1998);. Currently there seems to be no general procedure for copula selection agreed upon.…”

Section: Copula Familiesmentioning

confidence: 99%

“…Furthermore it allows to use predefined estimators for existing classes of marginal distributions and copula families (e.g. Fredricks and Nelsen, 2007). Although the IFM is a convenient approach, a major drawback is often overlooked (Mikosch, 2006a): It does not take into account, that the copula is determined by the parametric models for the margins, and is therefore dependent on their estimation.…”

Section: Estimation and Gof Testsmentioning

confidence: 99%

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Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Schölzel

Friederichs

2008

Nonlin. Processes Geophys.

287

178

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Abstract. Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.

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Section: Copula Familiesmentioning

confidence: 99%

Section: Estimation and Gof Testsmentioning

confidence: 99%

Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Schölzel

Friederichs

2008

Nonlin. Processes Geophys.

287

178

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“…d 1 = (1 − ρ S )/2 is a distance correlation measuring statistical dependence between two random variables, where ρ S is the Spearman's correlation between X and Y . Notice that d 1 can be expressed by using the copula C : Fredricks and Nelsen, 2007).…”

Section: A Distance Between Random Variablesmentioning

confidence: 99%

Toward a generic representation of random variables for machine learning

Marti¹,

Very

Donnat³

2016

Pattern Recognition Letters

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This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to represent random variables which splits apart dependency and distribution without losing any information. We also propound an associated metric leveraging this representation and its statistical estimate. Besides experiments on synthetic datasets, the benefits of our contribution is illustrated through the example of clustering financial time series, for instance prices from the credit default swaps market. Results are available on the website www.datagrapple.com and an IPython Notebook tutorial is available at www.datagrapple.com/Tech for reproducible research.

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“…First, there is no unique decision on the superiority of one of the measures. There are papers which compare these measures in the bivariate framework (Chen (2004), Durrleman, Nikeghbali and Roncalli (2000), Fredricks and Nelsen (2004), etc. ), however, nothing similar has been done in the multivariate case.…”

Section: For Different Generator Functions This Reduces To the Expresmentioning

confidence: 99%

Properties of hierarchical Archimedean copulas

Okhrin¹,

Okhrin²,

Schmid³

2013

Statistics &Amp; Risk Modeling

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In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

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On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables

Cited by 170 publications

References 11 publications

Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

Toward a generic representation of random variables for machine learning

Properties of hierarchical Archimedean copulas

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