There is an interesting connection between the Creasy-Williams confidence set of (12.2.24) and the interval CG() of (12.2.22). (a) Show that where is the MLE

There is an interesting connection between the Creasy-Williams confidence set of (12.2.24) and the interval CG() of (12.2.22).€ƒ
(a) Show that

where is the MLE of β and 2β is the previously defined consistent estimator of σ2β.
(b) Show that the Creasy-Williams set can be written in the form

Hence CG() can be derived by replacing the term in square brackets with 1, its probability limit. (In deriving this representation, the fact that and -1 / (λ) are roots of the numerator of rλ(β) is of great help. In particular, the fact that

is straightforward to establish.)

(8 B) |Ca(5) = {8: < Fin-2,0 (7 - u)/e