# Universal inference for variance components

## TL;DR

This paper develops finite-sample valid confidence intervals for variance components, especially near boundaries, with applications in genetics and mixed models, offering faster algorithms than existing methods.

## Contribution

It introduces novel universal inference methods for variance components near boundaries, improving accuracy and computational efficiency over existing approaches.

## Key findings

- Confidence intervals are valid in finite samples for boundary cases.
- Proposed algorithms are significantly faster than naive universal inference implementations.
- Methods are demonstrated effective through simulations and real data examples.

## Abstract

We consider universal inference in variance components models, focusing on settings where the parameter is near or at the boundary of the parameter set. Two cases, which are not handled by existing state-of-the-art methods, are of particular interest: (i) inference on a variance component when other variance components are near or at the boundary, and (ii) inference on near-unity proportions of variability, that is, one variance component divided by the sum of all variance components. Case (i) is relevant, for example, for the construction of componentwise confidence intervals, as often used by practitioners. Case (ii) is particularly relevant when making inferences about heritability in modern genetics. For both cases, we show how to construct confidence intervals that are uniformly valid in finite samples. We propose algorithms which, by exploiting the structure of variance components models, lead to substantially faster computing than naive implementations of universal inference. The usefulness of the proposed methods is illustrated by simulations and a data example with crossed random effects, which are known to be complicated for conventional inference procedures.