Inference for mixtures of symmetric distributions

Details Inference for mixtures of symmetric distributions Inference for mixtures of symmetric distributions

2007-08-03

arxiv.org/abs/0708.0499v1

Annals of Statistics 2007, Vol. 35, No. 1, 224-251

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001118 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001118

This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the component distributions. Because the class of symmetric distributions is so broad, identifiability of parameters is a major issue in these mixtures. We develop a notion of identifiability of finite mixture models, which we call k-identifiability, where k denotes the number of components in the mixture. We give sufficient conditions for k-identifiability of location mixtures of symmetric components when k=2 or 3. We propose a novel distance-based method for estimating the (location and mixing) parameters from a k-identifiable model and establish the strong consistency and asymptotic normality of the estimator. In the specific case of L_2-distance, we show that our estimator generalizes the Hodges--Lehmann estimator. We discuss the numerical implementation of these procedures, along with an empirical estimate of the component distribution, in the two-component case. In comparisons with maximum likelihood estimation assuming normal components, our method produces somewhat higher standard error estimates in the case where the components are truly normal, but dramatically outperforms the normal method when the components are heavy-tailed.

Affiliated with

Also associated with

No associations

Rating

Inference for mixtures of symmetric distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inference for mixtures of symmetric distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inference for mixtures of symmetric distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-602027