Sample d -copula of order m

José M. González-Barrios; María M. Hernández-Cedillo

Kybernetika (2013)

  • Volume: 49, Issue: 5, page 663-691
  • ISSN: 0023-5954

Abstract

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In this paper we analyze the construction of d -copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample d -copula of order m with m ≥ 2 , the central idea is to use the above methodologies to construct a new copula based on a sample. The greatest advantage of the sample d -copula is the fact that it is already an approximating d -copula and that it is easily obtained. We will see that these new copulas provide a nice way to study multivariate data with an approximating copula which is simpler than the empirical multivariate copula, and that the empirical copula is the restriction to a grid of a sample d -copula of order n . These sample d -copulas can be used to make statistical inference about the distribution of the data, as shown in Section 3.

How to cite

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González-Barrios, José M., and Hernández-Cedillo, María M.. "Sample $d$-copula of order $m$." Kybernetika 49.5 (2013): 663-691. <http://eudml.org/doc/260673>.

@article{González2013,
abstract = {In this paper we analyze the construction of $d$-copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample $d$-copula of order $m$ with $m≥2$, the central idea is to use the above methodologies to construct a new copula based on a sample. The greatest advantage of the sample $d$-copula is the fact that it is already an approximating $d$-copula and that it is easily obtained. We will see that these new copulas provide a nice way to study multivariate data with an approximating copula which is simpler than the empirical multivariate copula, and that the empirical copula is the restriction to a grid of a sample $d$-copula of order $n$. These sample $d$-copulas can be used to make statistical inference about the distribution of the data, as shown in Section 3.},
author = {González-Barrios, José M., Hernández-Cedillo, María M.},
journal = {Kybernetika},
keywords = {$d$-copulas; fractal copulas; sample $d$-copulas of order $m$; $d$-copulas; fractal copulas; sample $d$-copulas of order $m$},
language = {eng},
number = {5},
pages = {663-691},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Sample $d$-copula of order $m$},
url = {http://eudml.org/doc/260673},
volume = {49},
year = {2013},
}

TY - JOUR
AU - González-Barrios, José M.
AU - Hernández-Cedillo, María M.
TI - Sample $d$-copula of order $m$
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 5
SP - 663
EP - 691
AB - In this paper we analyze the construction of $d$-copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample $d$-copula of order $m$ with $m≥2$, the central idea is to use the above methodologies to construct a new copula based on a sample. The greatest advantage of the sample $d$-copula is the fact that it is already an approximating $d$-copula and that it is easily obtained. We will see that these new copulas provide a nice way to study multivariate data with an approximating copula which is simpler than the empirical multivariate copula, and that the empirical copula is the restriction to a grid of a sample $d$-copula of order $n$. These sample $d$-copulas can be used to make statistical inference about the distribution of the data, as shown in Section 3.
LA - eng
KW - $d$-copulas; fractal copulas; sample $d$-copulas of order $m$; $d$-copulas; fractal copulas; sample $d$-copulas of order $m$
UR - http://eudml.org/doc/260673
ER -

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