On a Flexible Information Criterion for Order Selection in
Semiparametric Mixture Models
An important yet difficult problem in fitting mixture models is
consistent estimation of the mixture complexity. Lindsay (1983) developed an elegant framework for nonparametric estimation of themixing distribution (consequently of the order) in the absence of a structural parameter (example, variance in a normal mixture) common to all component densities. However, under fairly general conditions,
incorporating a structural parameter results in nonexistence of the semiparametric estimator or in a degenerate semiparametric estimator. In effect, a different paradigm is required to accommodate the presence of a structural parameter in the mixture model. In this talk, we introduce a flexible information criterion (FLIC) by which the order
of a mixture model, mixing distribution and the structural parameter are consistently estimated. The FLIC is adaptive in the sense that the strength of the penalty is determined by the data, a feature lacked by the AIC and BIC. We show the performance of the FLIC through simulation experiments and applications to real data sets.
(Joint with Richard Charnigo, University of Kentucky.)