The Consistency of Estimators in Finite Mixture Models

Liu, W.B. and Cheng, R.C.H. (2001) The Consistency of Estimators in Finite Mixture Models. Scandinavian Journal of Statistics, 28 (4). pp. 603-616. ISSN 0303-6898 . (The full text of this publication is not available from this repository)

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Abstract

The parameters of a finite mixture model cannot be consistently estimated when the data come from an embedded distribution with fewer components than that being fitted, because the distribution is represented by a subset in the parameter space, and not by a single point. Feng & McCulloch (1996) give conditions, not easily verified, under which the maximum likelihood (MI.) estimator will converge to an arbitrary point in this subset. We show that the conditions can be considerably weakened. Even though embedded distributions may not be uniquely represented in the parameter space, estimators of quantities of interest, like the mean or variance of the distribution, may nevertheless actually be consistent in the conventional sense. We give an example of some practical interest where the ML estimators are rootn-consistent. Similarly consistent statistics can usually be found to test for a simpler model vs a full model. We suggest a test statistic suitable for a general class of model and propose a parameter-based bootstrap test, based on this statistic, for when the simpler model is correct.

Item Type: Article
Uncontrolled keywords: embedded model; indeterminacy; maximum likelihood; parametric bootstrap
Subjects: H Social Sciences > HA Statistics > HA33 Management Science
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Steve Wenbin Liu
Date Deposited: 03 Sep 2008 13:40
Last Modified: 14 Jan 2010 14:31
Resource URI: http://kar.kent.ac.uk/id/eprint/8488 (The current URI for this page, for reference purposes)
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