In Example 12.3.7, find F and G so that 0,1 and 1,0 are not 1/12, even when

Question:

In Example 12.3.7, find F and G so that ζ0,1 and ζ1,0 are not 1/12, even when P{X ≤ Y } = 1/2. Explore how large the rejection probability of the test with rejection region (12.46) can be under H 0. What does this imply about a Type 3 or directional error? That is, if the test rejects H 0 and then declares θ(F, G) > 1/2 because

√m(Un − 1/2) ≥

1 + λ

12 z1− α

2 , then how large can this probability be even if P{X ≤ Y } < 1/2?

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