Minimum Variance Unbiased Estimate of a Coverage Probability

Let F(x, θ) denote the distribution function of a vector variate x, whose range does not depend on the parameter θ. Then assuming that θ admits a complete and sufficient estimator θ̂, we derive minimum variance unbiased estimate of Px ≦ a= F(a, θ), where a is a known vector. The result is applied to a coverage problem in a normal set up.