Confidence Sets

Various methods of constructing confidence sets are introduced in this chapter, along with studies of properties of confidence sets. Throughout this chapter X = (X₁, …,X _n ) denotes a sample from a population P ∈ P; θ = θ(P) denotes a functional from P to Θ ⊂ R^k for a fixed integer k; and C(X) denotes a confidence set for θ, a set in ß_Θ (the class of Borel sets on Θ) depending only on X. We adopt the basic concepts of confidence sets introduced in §2.4.3. In particular, inf _P∈P P(θ ∈ C(X)) is the confidence coefficient of C(X) and, if the confidence coefficient of C(X) is ≥ 1- α for fixed α ∈ (0, 1), then we say that C(X) has significance level 1-α or C(X) is a level 1 - α confidence set.