A Note on NPML Estimation for Exponential Family Regression Models with Unspecified Dispersion Parameter


  • Jochen Einbeck National University of Ireland, Galway, Ireland
  • John Hinde National University of Ireland, Galway, Ireland




Nonparametric maximum likelihood (NPML) estimation for exponential families with unspecified dispersion parameter ? suffers from computational instability, which can lead to highly fluctuating EM trajectories and suboptimal solutions, in particular when ? is allowed to vary over mixture components. In this paper, a damped version of the EM algorithm is
proposed to cope with these problems.


Abramowitz, M., and Stegun, I. A. (1970). Handbook of Mathematical Functions. Dover.

Aitchison, J., and Aitken, C. G. G. (1976). Multivariate binary discrimination by kernel method. Biometrika, 63, 413-420.

Aitkin, M. (1996). A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing, 6, 251-262.

Aitkin, M. (2001). Likelihood and Bayesian analysis of mixtures. Statistical Modelling, 1, 287-304.

Aitkin, M., and Francis, B. (1995). Fitting overdispersed generalized linear models by nonparametric maximum likelihood. The GLIM Newsletter, 25, 37-45.

Aitkin, M., Francis, B., and Hinde, J. (2005). Statistical Modelling in GLIM 4. Oxford, UK: Oxford Statistical Science Series.

Biernacki, C., and Chretien, S. (2003). Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM. Statistics & Probability Letters, 61, 373-382.

Böhning, D. (1999). Computer-Assisted Analysis of Mixtures and Applications. Meta-Analysis, Disease Mapping and others. Boca Raton: Chapman & Hall / CRC.

Böhning, D., Schlattmann, P., and Lindsey, B. (1992). Computer-assisted analysis of mixtures (C.A.MAN): statistical algorithms. Biometrics, 48, 283-303.

Hinde, J. (1982). Compound Poisson regression models. In R. Gilchrist (Ed.), GLIM 82: Proceedings of the International Conference on Generalized Linear Models (Vol. 14, p. 109-121). New York: Springer-Verlag.

Laird, N. M. (1978). Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73, 805–811.

Ma, J., and Xu, L. (2005). Asymptotic convergence properties of the EM algorithm with respect to overlap in the mixture. Neurocomputing, 68, 105-129.

Postman, M., Huchra, J. P., and Geller, M. J. (1986). Probes of large-scale structures in the Corona Borealis region. Astronomical Journal, 92, 1238-1247.

Rosner, B. (2000). Fundamentals of Biostatistics. Duxbury, CA, USA: Duxbury Thomson Learning.




How to Cite

Einbeck, J., & Hinde, J. (2016). A Note on NPML Estimation for Exponential Family Regression Models with Unspecified Dispersion Parameter. Austrian Journal of Statistics, 35(2&3), 233–243. https://doi.org/10.17713/ajs.v35i2&3.369