Some New Copula Based Distribution-free Tests of Independence among Several Random Variables

Angshuman Roy (), Anil K. Ghosh (), Alok Goswami () and C. A. Murthy ()
Additional contact information
Angshuman Roy: Indian Statistical Institute
Anil K. Ghosh: Indian Statistical Institute
Alok Goswami: Indian Statistical Institute
C. A. Murthy: Indian Statistical Institute

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 7, 556-596

Abstract: Abstract Over the last couple of decades, several copula based methods have been proposed in the literature to test for independence among several random variables. But these existing tests are not invariant under monotone transformations of the variables, and they often perform poorly if the dependence among the variables is highly non-monotone in nature. In this article, we propose a copula based measure of dependency and use it to construct some distribution-free tests of independence. The proposed measure and the resulting tests, all are invariant under permutations and strictly monotone transformations of the variables. Our dependency measure involves a kernel function with an associated bandwidth parameter. We adopt a multi-scale approach, where we look at the results obtained for several choices of the bandwidth and aggregate them judiciously. Large sample properties of the dependency measure and the resulting tests are derived under appropriate regularity conditions. Several simulated and real data sets are analyzed to compare the performance of the proposed tests with some popular tests available in the literature.

Keywords: Gaussian kernel; Invariance; Large sample consistency; Measure of dependency; Multi-scale approach; Primary 62G10; 62H15; Secondary 62G20; 62H10 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-020-00207-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00207-2

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-020-00207-2

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().