Shortest two-tailed confidence intervals (Q1363821)

The authors derive a general method for computing the two-tailed shortest confidence interval (SCI) of an unknown parameter given the exact probability density function of a point estimator. The method, which they call `the optimal ratio method', is a generalization of the traditional equal-tails method; the upper and lower limits are chosen as to minimize the length of the confidence interval by controlling the ratio dividing the tail probabilities \(k\alpha\) and \((1-k)\alpha\). It is applied to two examples: the Pearson and the squared multiple correlations.