Prepivoting composite score statistics by weighted bootstrap iteration

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.