Powerful kernel‐based association tests for multivariate responses

Mingya Long, Yuke Shi, Liuquan Sun and Qizhai Li

Scandinavian Journal of Statistics, 2026, vol. 53, issue 2, 848-882

Abstract: In modern statistics, testing for dependence is often essential. The complex relationships between covariates and response variables present significant analytical challenges. While kernel‐based independence analysis has become a powerful alternative to tackle these issues, there is currently no universally effective kernel‐based test available. We introduce a series of kernel‐based independence tests within the framework of reproducing kernel Hilbert spaces (RKHS). This work includes explicit sample‐level expressions for these tests, as well as their asymptotic null distributions. Additionally, we develop two specific tests: The Maximal Kernel‐based Independence Test (MKIT) and the Maximin Efficient Robust Test (MERT), both of which are derived from the broader category of kernel‐based independence tests. Theoretically, we prove that MKIT and MERT asymptotically conform to the extreme‐value type I‐Gumbel distribution and the normal distribution under certain regular conditions, respectively, and analyze the powers of MKIT and MERT. We conduct extensive simulations that show that MKIT and MERT outperform numerous existing methods across various scenarios. Applications to heterogeneous stock mice data and human connectome project data further highlight the superior performance of the proposed test methods.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/sjos.70064

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:bla:scjsta:v:53:y:2026:i:2:p:848-882

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().