Abstract
An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, T.W. (1984).An Introduction to Multivariate Statistical Analysis, 2nd ed., John Wiley, New York.
Billingsley, P. (1986).Probability and Measure, 2nd ed., John Wiley, New York.
Chen, H., Chen, J. and Kalbfleisch, J.D. (2001). A modified likelihood test for homogeneity in finite mixture models.Journal of the Royal Statistical Society: Series B 63, 19–29.
Chen, J. and Kalbfleisch, J.D. (1996). Penalized minimum-distance estimates in finite mixture models,The Canadian Journal of Statistics,24, 167–175.
Feng, Z.D. and McCulloch, C.E. (1994). On the likelihood ratio test statistic for the number of components in a normal mixture with unequal variance,Biometrics,50, 1158–1162.
Garel, B. (2001). Likelihood ratio test for univariate Gaussian mixture,Journal of Statistical Planning and Inference,96, 325–350.
Henna, J. (1985). On estimating of the number of constituents of a finite mixture of constinuous distributions.Annals of the Institute of Statistical Mathematics 37, 235–240.
Henna, J. (2001). Marginal distributions of finite mixtures of multivariate normal distributions.Journal of the Japan Statistical Society,31, 187–191.
Keribin, C. (2000). Consistent estimation of the order of mixture models.Sankhya,62, 49–66.
McLachlan, G.J. and Basford, K.E. (1988).Mixture Models, Marcel Dekker, New York.
McLachlan, G. and Peel, D. (2000).Finite Mixture Models, John Wiley, New York.
Richardson, S. and Green, P.J. (1997) On Bayesian, analysis of mixtures with an unknown number of components,Journal of the Royal Statistical Society: Series B 59, 731–792.
Teicher, H. (1963). Identifiability of finite mixtures,The Annals of Mathematical Statistics,34, 1265–1269.
Titterington, D.M. (1990). Some recent research in the analysis of mixture distributions,Statistics,21, 619–641.
Titterington, D.M.et al. (1985).Statistical Analysis of Finite Mixture Distributions, John Wiley, New York.
Yakowitz, S.J. and Spragins, J.D. (1968). On the identifiability of finite mixtures,The Annals of Mathematical Statistics,39, 209–214.
Author information
Authors and Affiliations
About this article
Cite this article
Henna, J. Estimation of the number of components of finite mixtures of multivariate distributions. Ann Inst Stat Math 57, 655–664 (2005). https://doi.org/10.1007/BF02915431
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02915431