Advertisement

Statistics and Computing

, Volume 3, Issue 3, pp 103–108 | Cite as

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

  • Olcay Arslan
  • Patrick D. L. Constable
  • John T. Kent
Papers

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.

Keywords

Iterative reweighting algorithm robustness t-distribution updating function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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
  3. 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
  4. 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
  5. Huber, P. J. (1981) Robust Statistcs. Wiley, New York.Google Scholar
  6. 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
  7. Little, R. J. A. and Rubin, D. B. (1987) Statistical Analysis with Missing Data. Wiley, New York.Google Scholar
  8. Wu, C. F. J. (1983) On the convergence properties of the EM algorithms, Annals of Statistics, 11, 95–103.Google Scholar

Copyright information

© Chapman & Hall 1993

Authors and Affiliations

  • Olcay Arslan
    • 1
  • Patrick D. L. Constable
    • 1
  • John T. Kent
    • 1
  1. 1.Department of StatisticsUniversity of LeedsLeedsUK

Personalised recommendations