Simultaneous likelihood-based bootstrap confidence sets for a large number of models

Understand

The paper studies a problem of constructing simultaneous likelihood-based confidence sets.

• We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity.
• Theoretical results state the bootstrap validity in the following setting: the sample size \(n\) is fixed, the maximal parameter dimension \(p_{\textrm{max}}\) and the number of considered parametric models \(K\) are s.t.
• \((\log K)^{12}p_{\max}^{3}/n\) is small.