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Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

Danang Teguh Qoyyimi, Ricardas Zitikis (2015)

Dependence Modeling

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education,which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paperwe explore a novel approach based on a LOCindex,which is...

Medida de asociación propia entre variables aleatorias discretas.

María del Carmen Carollo Limeres (1984)

Trabajos de Estadística e Investigación Operativa

En este trabajo estudiamos la asociación entre dos variables aleatorias discretas (no cardinales) definiendo una nueva medida [de] asociación, la cual está basada en la velocidad de convergencia del vector de probabilidad correspondiente a la cadena de Markov asociada a la distribución de probabilidad conjunta de las variables en estudio. Ponemos especial énfasis en el estudio muestral y propiedades de los estimadores de dicha medida, calculando sus distribuciones asintóticas bajo el muestreo multinomial...

Medidas de asociación y dependencia bi-variante.

Concepción Fernández Vivas (1983)

Trabajos de Estadística e Investigación Operativa

El interrogante que vertebra este trabajo puede formularse así:¿Bajo qué condiciones es invertible la implicación X(ω), Y(ω) independientes ⇒ cov (X, Y) = 0 para v.a. no normales?La literatura estadística de los últimos años contiene en forma dispersa modelos interesantes de interdependencia de v.a. que adecuadamente combinados con la incorrelación pueden conducir a la independencia en situaciones de no-gaussianidad. Nuestra intención aquí es agruparlos sistemáticamente, ofreciéndolos en una línea...

Models gràfics d'independència.

Josep Maria Durán Rúbies (1999)

Qüestiió

Los modelos gráficos de independencia son una herramienta del análisis multivariante que utiliza gráficos para representar modelos. En particular, los grafos de independencia resumen y clarifican las interacciones entre variables, interacciones no siempre fáciles de interpretar, especialmente cuando en ellas intervienen tres o más variables.En este trabajo se proporciona, en clave pedagógica, una introducción a la teoría de grafos de independencia, comenzando por las nociones de independencia necesarias...

Multivariate extensions of expectiles risk measures

Véronique Maume-Deschamps, Didier Rullière, Khalil Said (2017)

Dependence Modeling

This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

Multivariate measures of concordance for copulas and their marginals

M. D. Taylor (2016)

Dependence Modeling

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.

N-dimensional measures of dependence.

Edward F. Wolff (1980)

Stochastica

In recent joint papers with B. Schweizer, we used the notion of a copula to introduce a family of symmetric, nonparametric measures of dependence of two random variables. Here, we present n-dimensional extensions of these measures and of Spearman's ro. We study them vis-a-vis appropriate higher dimensional analogues of Rényi's axioms for measures of dependence, determine relations among them, and in some cases establish reduction formulae for their computation.

New copulas based on general partitions-of-unity and their applications to risk management

Dietmar Pfeifer, Hervé Awoumlac Tsatedem, Andreas Mändle, Côme Girschig (2016)

Dependence Modeling

We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.

On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

Elena Di Bernardino, Didier Rullière (2016)

Dependence Modeling

An important topic in Quantitative Risk Management concerns the modeling of dependence among risk sources and in this regard Archimedean copulas appear to be very useful. However, they exhibit symmetry, which is not always consistent with patterns observed in real world data. We investigate extensions of the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based on the observation that when applied to the copula the inverse function of the generator of an...

On Bartlett's test for correlation between time series

Jiří Anděl, Jaromír Antoch (1998)

Kybernetika

An explicit formula for the correlation coefficient in a two-dimensional AR(1) process is derived. Approximate critical values for the correlation coefficient between two one-dimensional AR(1) processes are tabulated. They are based on Bartlett’s approximation and on an asymptotic distribution derived by McGregor. The results are compared with critical values obtained from a simulation study.

On copulas that generalize semilinear copulas

Juan Fernández Sánchez, Manuel Úbeda-Flores (2012)

Kybernetika

We study a wide class of copulas which generalizes well-known families of copulas, such as the semilinear copulas. We also study corresponding results for the case of quasi-copulas.

On extremal dependence of block vectors

Helena Ferreira, Marta Ferreira (2012)

Kybernetika

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to...

On measures of concordance.

Marco Scarsini (1984)

Stochastica

We give a general definition of concordance and a set of axioms for measures of concordance. We then consider a family of measures satisfying these axioms. We compare our results with known results, in the discrete case.

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