Many advanced statistical textbooks present the properties of asymptotic confidence regions, but most do not present methods of their numerical construction. In this work we present the concept of numerical computation of such regions and propose a method for its optimization. When constructing confidence regions for a selected parameter using an invariant test statistic, we may use a simple transformation, which allows us to compute the boundary of the confidence region with each computation and thus greatly reduce computation time. The concept is theoretically and practically interesting, as it gives us a method by which we can effectively construct confidence regions for the purposes of comparison or visualization. We also present a concrete implementation of the concept in the two-dimensional case for two different test statistics.
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