Computing the Standards Errors of Mixture Model Parameters with EM when Classes are Well Separated

Michel Wedel
Additional contact information
Michel Wedel: University of Groningen

Computational Statistics, 2001, vol. 16, issue 4, No 4, 539-558

Abstract: Summary It is shown that for finite mixtures the missing information tends to zero as the number of observations on each subject increases. Then, the classes become perfectly separated (i.e. the posterior membership probabilities are close to 0 or 1), the observed information tends to the complete information and the class-specific parameters in the mixture model become information orthogonal across classes. Then the asymptotic standard errors of parameter estimates can be obtained directly from the EM algorithm. The degree of class-separation is derived for which the amount of missing observation is approximately negligible and the asymptotic standard errors based on the complete information matrix are sufficiently accurate. Empirical illustrations are provided. A Monte Carlo study is performed to examine the extent to which the approximation is adequate. A comparison is made with other methods to approximate the observed information matrix. It is concluded that if the entropy of the posterior probabilities is larger than 0.95 the proposed approximation is reasonably accurate.

Keywords: Mixture Models; EM algorithm; Observed Information; Complete Information; Missing Information; Information Orthogonality; Entropy (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s180-001-8329-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:compst:v:16:y:2001:i:4:d:10.1007_s180-001-8329-3

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s180-001-8329-3

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().