1. Order selection with confidence for finite mixture models
- Author
-
Hien D. Nguyen, Daniel Fryer, Geoffrey J. McLachlan, La Trobe University [Melbourne], University of Queensland [Brisbane], and Nguyen, Hien
- Subjects
FOS: Computer and information sciences ,[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI] ,Statistics and Probability ,[STAT.AP]Statistics [stat]/Applications [stat.AP] ,[INFO.INFO-IM] Computer Science [cs]/Medical Imaging ,[INFO.INFO-NE] Computer Science [cs]/Neural and Evolutionary Computing [cs.NE] ,[SCCO.COMP]Cognitive science/Computer science ,[INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG] ,[STAT.OT]Statistics [stat]/Other Statistics [stat.ML] ,[INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE] ,[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] ,[STAT.OT] Statistics [stat]/Other Statistics [stat.ML] ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Physics::Geophysics ,[INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] ,Methodology (stat.ME) ,[STAT.AP] Statistics [stat]/Applications [stat.AP] ,[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] ,[SCCO.COMP] Cognitive science/Computer science ,[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] ,[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA] ,[INFO.INFO-IM]Computer Science [cs]/Medical Imaging ,[INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT] ,[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation ,Statistics - Methodology - Abstract
The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that allows for confidence statements to be made regarding the order of a finite mixture model. We construct finite sample tests, via data splitting and data swapping, for use in the STP, and we prove that such tests are consistent against fixed alternatives. Simulation studies and real data examples are used to demonstrate the performance of the finite sample tests-based STP, yielding practical recommendations of their use as confidence estimators in combination with point estimates such as the Akaike information or Bayesian information criteria. In addition, we demonstrate that a modification of the STP yields a method that consistently selects the order of a finite mixture model, in the asymptotic sense. Our STP is not only applicable for order selection of finite mixture models, but is also useful for making confidence statements regarding any sequence of nested models.
- Published
- 2022