Non-parametric tests for the tail equivalence via empirical likelihood

Yuexiang Jiang, Haoze Sun, Yi Zhang and Huaigang Long

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 21, 10640-10656

Abstract: In this paper, the problem of whether the left tail and the right tail of a distribution share the same extreme value index (EVI) is addressed and we propose two different test statistics. The first one is based on the result of the joint asymptotic normality of the two Hill estimators for the EVIs of both tails. And therefore, we can construct a quotient-type test statistic, which is asymptotic χ2(1) distributed after some standardization. The second test statistic proposed in this paper is inspired by the two-sample empirical likelihood methodology, and we prove its non parametric version of Wilk’s theorem. At last, we compare the efficiencies of our two test statistics and the maximum likelihood (ML) ratio test statistic proposed by Jondeau and Rockinger (2003) in terms of empirical first type error and power through a number of simulation studies, which indicate that the performance of the ML ratio test statistic is worse than our two test statistics in most cases.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2016.1242736 (text/html)
Access to full text is restricted to subscribers.

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:taf:lstaxx:v:46:y:2017:i:21:p:10640-10656

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2016.1242736

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().