Prepivoting composite score statistics by weighted bootstrap iteration

TL;DR

This paper explores using bootstrap methods to improve the accuracy of composite likelihood ratio tests and confidence regions, which often deviate from their nominal levels due to unknown parameters.

Contribution

It introduces prepivoting with weighted bootstrap iteration to enhance the reliability of composite score-based inference.

Findings

Bootstrap-based prepivoted tests are more accurate than asymptotic ones.

The method is computationally efficient and improves confidence set coverage.

Simulation studies demonstrate the effectiveness of the approach.

Abstract

The role played by the composite analogue of the log likelihood ratio in hypothesis testing and in setting confidence regions is not as prominent as it is in the canonical likelihood setting, since its asymptotic distribution depends on the unknown parameter. Approximate pivots based on the composite log likelihood ratio can be derived by using asymptotic arguments. However, the actual distribution of such pivots may differ considerably from the asymptotic reference, leading to tests and confidence regions whose levels are distant from the nominal ones. The use of bootstrap rather than asymptotic distributions in the composite likelihood framework is explored. Prepivoted tests and confidence sets based on a suitable statistic turn out to be accurate and computationally appealing inferential tools.