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Consider again the conditions of Exercise 19. Suppose now that θ is a real-valued parameter, and the following hypotheses are to be tested:
H0: θ = θ0,
H1: θ ≠ θ0.
Assume that θ0 is an interior point of the parameter space Ω. Show that if the test procedure δ is unbiased and if its power function π(θ|δ) is a differentiable function of θ, then π (θ0|δ) = 0, where π (θ0|δ) denotes the derivative of π(θ|δ) evaluated at the point θ = θ0. |
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