Testing linear combinations of multiple variance components
Abstract
We test the hypothesis that simulataneous linear contrasts of multiple variance components equal zero in a Gaussian variance components model via a parametric bootstrap. Applications include but are not limited to nested and crossed designs. The main technical contributions are a computationally efficient decomposition of the normalized residual log-likelihood that does not require the variance components to be non-negative or variance design matrices to be positive semi-definite, a modified Newton method for its minimization, and a method for efficient optimization and sampling under the null hypothesis that certain linear combinations of variance components equal zero. A special case of the proposed procedure is a test for multiple variance components simulataneously equalling zero, for which a likelihood ratio test was not previously available. However, the proposed procedure is significantly more general.
Keywords
Cite
@article{arxiv.2604.25744,
title = {Testing linear combinations of multiple variance components},
author = {Alex Stringer and Jeffrey Negrea},
journal= {arXiv preprint arXiv:2604.25744},
year = {2026}
}