As in Example 13.5.7, consider testing = 0 versus = 0. Suppose n is asymptotically level and asymptotically unbiased in the sense

As in Example 13.5.7, consider testing θ = θ0 versus θ = θ0.

Suppose φn is asymptotically level α and asymptotically unbiased in the sense lim inf n Eθ0+hn−1/2 (φn) ≥ α

for any h = 0. Argue that, among such tests φn, the two-sided Rao test φn,2 is LAUMP.