  Mixture models are becoming a popular tool for the clustering and
classification of high-dimensional data. In such high dimensional applications,
model selection is problematic. The Bayesian information criterion, which is
popular in lower dimensional applications, tends to underestimate the true
number of components in high dimensions. We introduce an adaptive
LASSO-penalized BIC (ALPBIC) to mitigate this problem. This efficacy of the
ALPBIC is illustrated via applications of parsimonious mixtures of factor
analyzers. The selection of the best model by ALPBIC is shown to be consistent
with increasing numbers of observations based on simulated and real data
analyses.
