Title: More sensitive mixture detection using the empirical moment-generating function
Authors: Michael Stewart - University of Sydney (Australia) [presenting]
Thomas Porter - University of Melbourne (Australia)
Abstract: The higher criticism method was originally developed as a goodness of fit test to the uniform distribution with focus on multiple testing of a large number of independent p-values. It was shown early on to have very good performance when testing for a certain kind of normal location mixture, indeed it has the same lower-order power properties as a (generalised) likelihood ratio test. It has since been further developed into a tool for feature selection in high-dimensional classification problems and has been shown to have excellent performance in that setting also, both theoretically and according to some well-regarded benchmarking procedures. We provide a higher-order power analysis comparing higher criticism with the generalised likelihood ratio test and another easier-to-implement test based on the empirical moment-generating function, which shows that the latter two tests are optimal in a certain minimax sense whereas higher criticism is not. We also provide some guidance for when to use which method.