Abstract
The paper compares several versions of the likelihood ratio test for exponential homogeneity against mixtures of two exponentials. They are based on different implementations of the likelihood maximization algorithm. We show that global maximization of the likelihood is not appropriate to obtain a good power of the LR test. A simple starting strategy for the EM algorithm, which under the null hypothesis often fails to find the global maximum, results in a rather powerful test. On the other hand, a multiple starting strategy that comes close to global maximization under both the null and the alternative hypotheses leads to inferior power.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Böhning, D., Dietz, E., Schaub, R., Schlattmann, P., Lindsay, B. G. (1994). The Distribution of the Likelihood Ratio for Mixtures of Densities from the One-Parameter Exponential Family.Ann. Institute Statistical Mathematics 46, 373–388.
Bozdogan, H. (1993): Choosing the number of component clusters in the mixture-model using a new informational complexity criterion of the inverse Fisher information matrix, pp 40–54 inInformation and Classification, (ed. O. Opitz, B. Lausen, R. Klar). Berlin: Springer Verlag.
Dacunha-Castelle, D., Gassiat, E. (1997a). The estimation of the order of a mixture model,Bernoulli 3, 279–299.
Dacunha-Castelle, D., Gassiat, E. (1997b). Testing in locally conic models, and application to mixture models.ESAIM: Probability and Statistics 1, 285–317.
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion).J. Royal Statistical Soc. B 39, 1–38.
Everitt, B.S., Hand, D.J. (1981).Finite Mixture Distributions. London: Chapman and Hall.
Hasselblad, V. (1982). Estimation of finite mixtures of distributions from the exponential family.J. American Statistical Association 64, 1459–1471.
Jewell, N.P. (1982). Mixtures of exponential distribution.Ann. Statistics 10, 479–484.
Kaylan, A.R., Harris, C.M. (1981). Efficient algorithms to derive maximum likelihood estimates for finite exponential and Weibull distributions.Computers and Operations Research 8, 97–104.
Lindsay, B.G. (1995).Mixture Models: Theory, Geometry and Applications. Hayward, California: Institute of Mathematical Statistics.
Maller, R.A., Zhou, X. (1996).Survival Analysis with Long-Time Survivors. Chichester: J. Wiley.
Meilijson, I. (1989). A fast improvement to the EM algorithm on its own terms.Journal Royal Statistical Soc. B 51, 127–138.
McLachlan, G.J. (1995): Mixtures—Models and Applications, chapter 19 inThe Exponential Distribution (eds. N. Balakrishnan, A.P. Basu). Amsterdam: Gordon and Breach.
McLachlan, G.J., Krishnan, T. (1997).The EM Algorithm and Extensions. New York: J. Wiley.
Richardson, S., Green, P.J. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion).J. Royal Statistical Soc. B 59, 731–792.
Robert, C. (1996). Mixtures of distributions: Inference and estimation, pp 441–464 inPractical Markov Chain Monte Carlo, (eds. W.R. Gilks, S. Richardson, D.J. Spiegelhalter). London: Chapman and Hall.
Titterington, D.M., Smith, A.F.M., Makov, U.E. (1985).Statistical Analysis of Finite Mixture Distributions. Chichester: J. Wiley.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seidel, W., Mosler, K. & Alker, M. Likelihood ratio tests based on subglobal optimization: A power comparison in exponential mixture models. Statistical Papers 41, 85–98 (2000). https://doi.org/10.1007/BF02925678
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02925678