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Consider a problem of testing hypotheses in which the following hypotheses about an arbitrary parameter θ are to be tested:
H0: θ ∈ Ω0,
H1: θ ∈ Ω1.
Suppose that δ is a test procedure of size α (0 < α < 1) based on some vector of observations X, and let π(θ|δ) denote the power function of δ. Show that if δ is unbiased, then π(θ|δ) ≥ α at every point θ ∈ Ω1. |
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