Penalized minimum‐distance estimates in finite mixture models

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Abstract
When finite mixture models are used to fit data, it is sometimes important to estimate the number of mixture components. A nonparametric maximum‐likelihood approach may result in too many support points and, in general, does not yield a consistent estimator. A penalized likelihood approach tends to produce a fit with fewer components, but it is not known whether that approach produces a consistent estimate of the number of mixture components. We suggest the use of a penalized minimum‐distance method. It is shown that the estimator obtained is consistent for both the mixing distribution and the number of mixture components.

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