An adaptive test based on Kendall's tau for independence in high dimensions

Xiangyu Shi, Yuanyuan Jiang, Jiang Du and Zhuqing Miao

Journal of Nonparametric Statistics, 2024, vol. 36, issue 4, 1064-1087

Abstract: We consider testing the mutual independency for high-dimensional data. It is known that $ L_2 $ L2-type statistics have lower power under sparse alternatives and $ L_\infty $ L∞-type statistics have lower power under dense alternatives in high dimensions. In this paper, we develop an adaptive test based on Kendall's tau to compromise both situations of the alternative, which can automatically be adapted to the underlying data. An adaptive test is very useful in practice as the sparsity or density for a data set is usually unknown. In addition, we establish the asymptotic joint distribution of $ L_2 $ L2-type and $ L_\infty $ L∞-type statistics based on Kendall's tau under mild assumptions and the asymptotic null distribution of the proposed statistic. Simulation studies show that our adaptive test performs well in either dense or sparse cases. To illustrate the usefulness and effectiveness of the proposed test, real data sets are also analysed.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2023.2296521 (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:gnstxx:v:36:y:2024:i:4:p:1064-1087

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2023.2296521

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().