Uniformly most accurate confidence intervals under weak restrictions

The natural and commonly used measure of accuracy for a confidence interval (CI) is its length, but it only applies to bounded CI's. More seriously, it is not an invariant measure, creating chaos on selecting CI's. Using the probability of false coverage as a finite and invariant measure of accuracy for a CI, we establish the uniformly most accurate (UMA) CI under weak restriction, which substantially improves the classical UMA unbiased CI for simplicity and optimality.