The construction used in Theorem 5 applies more generally:
Given a confidence interval of the form In=In(γ⋆,π⋆,δ)
for some confidence level δ
and a fully empirical confidence set En(δ) for (γ⋆,π⋆) for the same level,
I′n=En(δ)∩∪(γ,π)∈En(δ)In(γ,π,δ) …