The University of Southampton
University of Southampton Institutional Repository

The consistency of estimators in finite mixture models

Cheng, R.C.H. and Liu, W.B. (2001) The consistency of estimators in finite mixture models Scandinavian Journal of Statistics, 28, (4), pp. 603-616. (doi:10.1111/1467-9469.00257).

Record type: Article


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 (ML) 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 root of n-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.

Full text not available from this repository.

More information

Published date: December 2001
Organisations: Operational Research


Local EPrints ID: 29719
ISSN: 0303-6898
PURE UUID: 65902004-23ec-49b2-8843-c7e670cb91e2

Catalogue record

Date deposited: 12 May 2006
Last modified: 17 Jul 2017 15:57

Export record



Author: R.C.H. Cheng
Author: W.B. Liu

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.