Kernel‐based marginal testing for covariate effects in high‐dimensional settings

Hong Yin, Yijun Wang and Ancha Xu

Scandinavian Journal of Statistics, 2026, vol. 53, issue 1, 498-531

Abstract: In high dimensions, the relationship between covariates and a response variable becomes increasingly intricate, with different covariate components often displaying varying degrees of variability. This complex interplay of dependence, heterogeneity, and high dimensionality presents a significant challenge when investigating the effects of covariates on the response variable. To address this, we propose a novel marginal testing procedure based on kernel‐based conditional mean dependence, which can be implemented without requiring model assumptions. Theoretically, we establish the limiting normal distributions of the test statistic under both null hypotheses and local alternatives by asymptotically approximating a class of quadratic forms. We also examine the asymptotic relative efficiency of the proposed test against several state‐of‐the‐art alternatives. Our theoretical evaluations are conducted from two perspectives: a detailed analysis within a linear model framework and a comparison within a fully non‐parametric setting. The effectiveness and applicability of the proposed method are demonstrated through both simulation studies and real data analysis.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/sjos.70049

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:1:p:498-531

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 ().