Skip to main content
SpringerLink
Log in

A Cautionary Note on Likelihood Ratio Tests in Mixture Models

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation. Different starting strategies and stopping rules yield completely different estimators of the parameters. This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm.

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

  • Böhning, D. and Schlattmann, P. (1992). Computer-Assisted Analysis of Mixtures (C.A.M.AN): Statistical algorithms, Biometrics, 48, 283–303.

    Google Scholar 

  • Böhning, D. and Schlattmann, P. (1997). Personal communication.

  • Böhning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. G. (1994). The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family, Ann. Inst. Statist. Math., 46, 373–388.

    Google Scholar 

  • Dempster, A. P., Laird, N. M. and Rubin, D. B. (1997). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. B, 39, 1–38.

    Google Scholar 

  • Everitt, B. S. and Hand, D. J. (1981). Finite Mixture Distributions, Chapman and Hall, London.

    Google Scholar 

  • Lindsay, B. G. (1995). Mixture Models: Theory, Geometry and Applications, Institute of Mathematical Statistics, Hayward, California.

    Google Scholar 

  • Lindstrom, M. J. and Bates, D. M., (1988). Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data, J. Amer. Statist. Assoc., 83, 1014–1022.

    Google Scholar 

  • McLachlan, G. J. and Basford, K. E., (1988). Mixture Models: Inference and Applications to Clustering, Marcel Dekker, New York.

    Google Scholar 

  • McLachlan, G. J. and Krishnan, T. (1997). The EM Algorithm and Extensions, Wiley, New York.

    Google Scholar 

  • Seidel, W., Mosler, K., Alker, M. and Ruck. A. (1997). Size and power of likelihood ratio tests in exponential mixture models based on different implementations of the EM algorithm, Discussion Papers in Statistics and Quantitative Economics, 79, Universität der Bundeswehr Hamburg.

  • Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985). Statistical Analysis of Finite Mixture Distributions, Wiley, Chichester.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Wirtschafts- und Organisationswissenschaften, Universität der Bundeswehr Hamburg, D-22039, Hamburg, Germany

    Wilfried Seidel & Manfred Alker

  2. Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, D-50923, Köln, Germany

    Karl Mosler

Authors
  1. Wilfried Seidel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Mosler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manfred Alker
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Seidel, W., Mosler, K. & Alker, M. A Cautionary Note on Likelihood Ratio Tests in Mixture Models. Annals of the Institute of Statistical Mathematics 52, 481–487 (2000). https://doi.org/10.1023/A:1004117419204

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004117419204

Search

Navigation