Fast and reliable confidence intervals for a variance component

TL;DR

This paper introduces a fast, reliable method for constructing confidence intervals for variance components using score-based test-statistics, effective even at parameter boundaries, with applications in spatial transcriptomics.

Contribution

The authors develop a new approach to confidence intervals for variance components that is both computationally efficient and accurate in small samples and boundary cases.

Findings

Method achieves near-nominal coverage in simulations.

Significantly faster than existing methods, up to 28,000 times.

Applicable to large-scale spatial transcriptomics data.

Abstract

We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results apply in settings where the variance is near or at the boundary of the parameter set. Simulations indicate the proposed test-statistics are approximately pivotal and lead to confidence intervals with near-nominal coverage even in small samples. We illustrate our methods' application in spatially-resolved transcriptomics where we compute approximately 15,000 confidence intervals, used for gene ranking, in less than 4 minutes. In the settings we consider, the proposed method is between two and 28,000 times faster than popular alternatives, depending on how many confidence intervals are computed.