Estimation of the Multivariate Extension of the Spearman-type Measure of Local Dependence (original) (raw)

Estimation of a Spearman-Type Multivariate Measure of Local Dependence

International Journal of Statistics and Probability, 2014

A multivariate measure of local dependence written in terms of copulas is proposed, which if integrated, coincides with a population version of a multivariate global measure of Spearman's rho. We propose nonparametric estimators of this measure for independent sample data and also for time series data. Some properties of the estimators are derived. Simulations with different copulas and sample sizes were performed to assess the theoretical findings. Empirical applications are given for selected economic indexes of some countries and for the returns of the DAX, CAC40 and FTSE indexes.

General Multivariate Dependence Using Associated Copulas

SSRN Electronic Journal, 2011

This paper studies the general multivariate dependence of a random vector using associated copulas. We extend definitions and results of positive dependence to the general dependence case. This includes associated tail dependence functions and associated tail dependence coefficients. We derive the relationships among associated copulas and study the associated copulas of the perfect dependence cases and elliptically contoured distributions. We present the expression for the associated tail dependence function of the multivariate Student-t copula, which accounts for all types of tail dependence. Date: April 20th, 2012. This paper is based on results from the first chapters of my doctorate thesis supervised by Dr. Wing Lon Ng. I would like to thank Mexico's CONACYT, for the funding during my studies. I would also like to thank my examiners Dr. Aristidis Nikoloulopoulos and Dr. Nick Constantinou for the corrections, suggestions and comments that have made this work possible.

Transfer of Global Measures of Dependence into Cumulative Local

Applied Mathematics-a Journal of Chinese Universities Series B, 2014

We explore an idea of transferring some classic measures of global dependence between random variables Χ1, Χ2, L, Χn into cumulative measures of dependence relative at any point (χ1, χ2, L, χn) in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.

A Copula Statistic for Measuring Nonlinear Multivariate Dependence

arXiv: Statistics Theory, 2016

A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us to define the CoS in terms of a relative distance function between the empirical copula, the Fr\'echet-Hoeffding bounds and the independence copula. Monte Carlo simulations reveal that for large sample sizes, the CoS is approximately normal. This property is utilised to develop a CoS-based statistical test of independence against various noisy functional dependencies. It is shown that this test exhibits higher statistical power than the Total Information Coefficient (TICe), the Distance Correlation (dCor), the Randomized Dependence Coefficient (RDC), and the Copula Correlation (Ccor) for monotonic and circular functional dependencies. Furthermore, the R2-equitability of the CoS is investigated for estimating the strength of a collection of fu...

On Nonsymmetric Nonparametric Measures of Dependence

Based on recent progress in research on copula based dependence measures, we review the original Rényi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures can actually better characterize the relationship between a pair of random variables including both independence and complete dependence. The new measures also satisfy the Data Processing Inequality (DPI) on the * product on copulas, which leads to nice features including the invariance of dependence measure under bijective transformation on one of the random variables. The issues with symmetric measures are also clarified.

A Copula-Based Non-parametric Measure of Regression Dependence

Scandinavian Journal of Statistics, 2012

This paper presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new nonparametric measure of regression dependence and study its properties. Beside being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent nonparametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of small simulation study.

Sibuyas Measure of Local Dependence

2008

Common measures of association quantify the global association between two variables, however, the data may have different behaviours of association or dependence if we consider subsets of the data. The aim of this paper is to study the function of local dependence of Sibuya (1960) for two continuous random variables. We rewrite this function in terms of copula. We propose three nonparametric estimators, deriving their respective properties. Simulations and applications to real data are also given.

Dependence measures for perturbations of copulas

Fuzzy Sets and Systems, 2017

In this paper (which is a substantially extended version of a conference paper from AGOP 2015 [10]), we investigate the effects of specific class of perturbations of bivariate copulas on several measures of dependence (Spearman's rho, Blomqvist's beta, Gini's gamma, Kendall's tau), and tail dependence along both diagonal sections. It is demonstrated that the influence of the perturbation parameter on the values of the first three of the above coefficients of dependence is linear, while on the last one it is quadratic. Interesting numerical analyses for several important classes of Archimedean copulas are presented. It is also demonstrated that the considered perturbations do not change the coefficients of tail dependencies along the main diagonal but linearly reduce their values along the second diagonal. An interesting possible application for analyzing dependencies along the second diagonal of copulas represent insurance data, where censoring introduces a negative dependence between the investigated components of the claims. As a by-product, we present a new class of perturbations of copulas that linearly reduce the more popular coefficients of tail dependencies along the main diagonal, while preserving their values along the second diagonal. Subsequently using suitable elements of both above classes of perturbations, any original copula can be transformed to a resulting one, having coefficients of tail dependencies along both diagonals linearly reduced (with any couple of preselected linear proportions from [0, 1]).