A1631
Title: Score test for order of finite normal mixtures
Authors: Junfan Tao - Kyoto University (Japan) [presenting]
Jiaying Gu - University of Toronto (Canada)
Pujee Tuvaandorj - York University (Canada)
Stanislav Volgushev - University of Toronto (Canada)
Abstract: Finite mixture models are widely used in empirical work, but determining the number of components remains a challenging problem. A score test for inference on the number of components is developed, drawing on Neymans C(alpha) framework. The test generalizes previous work, can be interpreted as a score test for neglected heterogeneity of multiple dimensions in finite Gaussian mixtures, and is closely related to the information matrix test for the same model. For a broad class of alternatives, the local expansion of the likelihood yields the same test statistic as in related likelihood-ratio-based inference on the order of finite Gaussian mixtures, thereby benefiting from the computational simplicity of a score test. A bootstrap-based implementation of the test is proposed and its consistency is established. The local asymptotic power envelope is characterized, which provides insight into its optimality. An empirical application illustrates the use of the proposed test.
