Goodness-of-fit testing for normal mixture densities

A novel goodness-of-fit test for assessing the validity of maximum likelihood estimates of normal mixture densities with known number of components is introduced. The theoretical contributions include analytic quantification of the test statistic's size and power functions under fixed and local alternatives. These are used to derive a closed-form bandwidth rule which optimizes the test's power while keeping its size constant at a given significance level, and a cut-off point suitable for finite sample implementations of the test. An extensive simulation study compares the performance of the new test to well-established tests in the literature and demonstrates the superiority of the former in all examples considered. Finally, its practical usefulness is demonstrated in the analysis of two real world datasets.& COPY; 2023 Elsevier B.V. All rights reserved.