Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM

Christophe Biernacki and Stéphane Chrétien

Statistics & Probability Letters, 2003, vol. 61, issue 4, 373-382

Abstract: As is well known, the likelihood in the Gaussian mixture is unbounded for any parameters such that a Dirac is placed at any observed sample point. The behavior of the EM algorithm near a degenerated solution is studied. It is established that there exists a domain of attraction around degeneracy and that convergence to these particular solutions is extremely fast. It confirms what many practitioners already noted in their experiments. Some available proposals to avoid degenerating are discussed but the presented convergence results make it possible to defend the pragmatic approach to the degeneracy problem in EM which consists in random restarts.

Keywords: Degeneracy; Maximum; likelihood; EM; algorithm; Gaussian; mixtures; Speed; of; convergence (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00396-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:61:y:2003:i:4:p:373-382

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().