부산대학교 도서관

Given a data set X ∼ Pψ,η and estimates ψ̂ and η̂ we are interested in confidence bounds for the real parameter ψ. Let Dψ,η(y) = Pψ,η(ψ̂ ≤ y) and assume that Dψ,η̂(ψ̂) is a pivot with pivot distribution H. Assume that Dψ,η̂(ψ̂) is nondecreasing in ψ for fixed ψ̂ and η̂. Then it is possible to construct exact, transformation equivariant confidence bounds for ψ. It is shown that a modified double bootstrap procedure yields exactly these bounds without knowledge of D or H, provided the number of bootstrap samples becomes infinite. Although the existence of exact pivots is special, it is plausible that the proposed method will yield approximate confidence bounds, when there are approximate local pivots. This aspect is explored analytically and by simulation in two examples.