6Hypothesis testing and model selection for mixture models
The Gaussian mixture models play important roles in statistical analysis. In fact, it is well known that any continuous distribution can be approximated well by a finite mixture of normal densities (Lindsay, 1995; McLachlan and Peel, 2000). When the number of components is unknown, one could use the nonparametric maximum likelihood estimate (NPMLE) introduced in Section 1.13 to estimate the mixing distribution nonparametrically. However, when the data has an underlying clustering structure, the NPMLE tends to overestimate the true number of components. If too many components are used, the mixture model may overfit the data and produce poor interpretations. ...
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