Comparison, utility, and partition of dependence under absolutely continuous and singular distributions

Nader Ebrahimi, Nima Y. Jalali and Ehsan S. Soofi

Journal of Multivariate Analysis, 2014, vol. 131, issue C, 32-50

Abstract: This paper first illustrates that a mutual information index detects and ranks dependence of a wide variety of absolutely continuous families, but the popular association and variance reduction indices fail to serve as such “common metrics”. We then elaborate on some theoretical merits of the mutual information and give several results. The mutual information provides a notion of the utility of dependence for predicting random variables and quantifies how much the joint distribution is more informative about the variables than the independent model. We present insightful partitions of dependence among the components of a random vector, for a class of models recently proposed for dependence of uncorrelated variables, and for the elliptical families. We also recall that the mutual information is not applicable to singular distributions and give some results for a generalized information index for these models. The generalized index is derived for the Marshall–Olkin copula and for a new singular copula that represents the dependence of the consecutive terms of the exponential autoregressive and related processes.

Keywords: Convolution; Copula; Entropy; Elliptical distribution; Marshall–Olkin; Mutual information; Predictability; Sarmanov families; Shock models; Utility (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X14001444
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:131:y:2014:i:c:p:32-50

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2014.06.014

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().