Skip to main content
SpringerLink
Log in

Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem

  • Papers
  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Beaton, A. E. and Tukey, J. W. (1974) The fittinHg of power series, meaning polynomials illustrated on band-spectroscopic data, Technometrics, 16, 147–193.

    Google Scholar 

  • Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, B 39, 1–38.

    Google Scholar 

  • Dempster, A. P., Laird, N. M. and Rubin, D. B. (1980) Iteratively reweighted least squares for linear regression where errors are normal/independent distributed, in Multivariate Analysis V (P. R. Krishnaiah, ed.), North-Holland, New York, pp. 35–37.

    Google Scholar 

  • Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986) Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.

    Google Scholar 

  • Huber, P. J. (1981) Robust Statistcs. Wiley, New York.

    Google Scholar 

  • Lange, K. L., Little, R. J. A., and Tylor, J. M. G. (1989) Robust and statistical modeling using the t-distribution, Journal of the American Statistical Association, 84, 881–896.

    Google Scholar 

  • Little, R. J. A. and Rubin, D. B. (1987) Statistical Analysis with Missing Data. Wiley, New York.

    Google Scholar 

  • Wu, C. F. J. (1983) On the convergence properties of the EM algorithms, Annals of Statistics, 11, 95–103.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Leeds, LS2 9JT, Leeds, UK

    Olcay Arslan, Patrick D. L. Constable & John T. Kent

Authors
  1. Olcay Arslan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick D. L. Constable
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John T. Kent
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arslan, O., Constable, P.D.L. & Kent, J.T. Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem. Stat Comput 3, 103–108 (1993). https://doi.org/10.1007/BF00147772

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00147772

Keywords

Search

Navigation