In signal detection (*) theory, this statement is equivalent to the maximization of the true positive rate for some upper bound on the false negative rate.
A result by Cvitanic and Karatzas used convex analysis to generalize this result to families of functions. A 1951 paper by Dantzig and Wald answered two questions left open by the paper that derived this result by demonstrating both an existence proof as well as a necessity and sufficiency proof. This result can be visualized by depicting it as an optimal receiver operating characteristic curve. In signal detection (*) theory, this statement is equivalent to the maximization of the true positive rate for some upper bound on the false negative rate. This statement was first introduced by its namesakes in the paper "On the Problem of the Most Efficient Tests of Statistical Hypotheses." For 10 points, identify this statement, which holds that for a given threshold and significance level, the likelihood ratio test that prefers one of two hypotheses depending on a critical value of a threshold is the most powerful one.
A result by Cvitanic and Karatzas used convex analysis to generalize this result to families of functions.
Neyman-Pearson lemma or theorem