Let X1,..., Xn; Y1,..., Yn be samples from N(, 2) and N(, 2), respectively. Then the

Let X1,..., Xn; Y1,..., Yn be samples from N(ξ, σ2) and N(η, τ 2), respectively. Then the confidence intervals (5.42) for τ 2/σ2, which can be written as

(Yj − Y¯)2 k

(Xi − X¯)2 ≤ τ 2

σ2 ≤

k

(Yj − Y¯)2

(Xi − X¯)2 , are uniformly most accurate equivariant with respect to the smallest group G containing the transformations X i = a X +

b, Y i = aY + c for all a = 0,

b, c and the transformation X i = dYi , Y i = Xi /d for all d = 0.

[Cf. Problem 6.12.]