Graph-theoretic Inference for Random Effects in High-dimensional Studies

Lynna Chu; Yichuan Bai

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arXiv · 2506.07946

Graph-theoretic Inference for Random Effects in High-dimensional Studies

Lynna Chu·Yichuan Bai

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Abstract

We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero. Our approach is non-parametric and model-free in the sense that we not require correct specification of the mixed model nor estimation of unknown parameters. Instead, the test statistic evaluates whether incorporating group-level correlation meaningfully improves the ability of a potentially high-dimensional covariate vector $X$ to predict a response variable $Y$. We establish the consistency of the proposed test and derive its asymptotic null distribution. Through simulation studies and a real data application, we demonstrate the practical effectiveness of the proposed test.

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BibTeX RIS

Lynna Chu, Yichuan Bai. 2025-06-09. Graph-theoretic Inference for Random Effects in High-dimensional Studies. https://arxiv.org/abs/2506.07946

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