Theory and Methods of Statistics

Theorem 6.12.2

If for each ${\theta }^{\prime }$, $A\left({\theta }^{\prime }\right)$ is the acceptance region of a UMP unbiased level α test for $H_0:\theta ={\theta }^{\prime }$ vs $H_1:\theta \ne {\theta }^{\prime }$, then C(x) = {θ: x ∈ A(θ)} is a UMA unbiased confidence interval for θ with confidence coefficient 1 − α.

[Analogous correspondence holds between acceptance regions of UMP unbiased level α tests for $H_0:\theta \le {\theta }^{\prime }$ vs $H_1:\theta >{\theta }^{\prime }$ and UMA unbiased ...