191
Views
1
CrossRef citations to date
0
Altmetric
Research Article

A nonparametric estimation method for the multivariate mixture models

&
Pages 3727-3742 | Received 08 Feb 2022, Accepted 27 May 2022, Published online: 13 Jun 2022

References

  • Everitt BS, Hand DJ. Finite mixture distributions. New York: Wiley; 1981.
  • Kasahara H, Shimotsu K. Non-parametric identification and estimation of the number of components in multivariate mixtures. J R Stat Soc Ser B. 2014;76(1):97–111.
  • Lindsay BG. Mixture models: theory, geometry and applications. Hayward: Institute of Mathematical Statistics; 1995.
  • McLachlan GJ, Basford KE. Mixture models: inference and applications to clustering. New York: Dekker; 1988.
  • McLachlan GJ, Peel D. Finite mixture models. New York: Wiley; 2000.
  • Titterington DM, Smith AFM, Makov UE. Statistical analysis of finite mixture distributions. New York: Wiley; 1985.
  • Zheng C, Wu Y. Nonparametric estimation of multivariate mixtures. J Am Stat Assoc. 2020;115(531):1456–1471.
  • Benaglia T, Chauveau D, Hunter DR. An EM-like algorithm for semi- and nonparametric estimation in multivariate mixtures. J Comput Graph Stat. 2009;18(2):505–526.
  • Allman ES, Matias C, Rhodes JA. Identifiability of parameters in latent structure models with many observed variables. Ann Stat. 2009;37(6A):3099–3132.
  • Benaglia T, Chauveau D, Hunter DR. Bandwidth selection in an EM-like algorithm for nonparametric multivariate mixtures. In: Hunter DR, Richards DSP, Rosenberg JL, editors. Nonparametrics and mixture models: a festschrift dedicated to Thomas P. Hettmansperger. Singapore: World Scientific Publishing; 2011.
  • Bonhomme S, Jochmans K, Robin JM. Estimating multivariate Latent-Structure models. Ann Stat. 2016;44(2):540–563.
  • Chauveau D, Hunter DR, Levine M. Semi-parametric estimation for conditional independence multivariate finite mixture models. Stat Surv. 2015;9:1–31.
  • Hall P, Neeman A, Pakyari R, et al. Nonparametric inference in multivariate mixtures. Biometrika. 2005;92(3):667–678.
  • Hall P, Zhou XH. Nonparametric estimation of component distributions in a multivariate mixture. Ann Stat. 2003;31(1):201–224.
  • Levine M, Hunter DR, Chauveau D. Maximum smoothed likelihood for multivariate mixtures. Biometrika. 2011;98(2):403–416.
  • Cruz-Medina IR, Hettmansperger TP, Thomas H. Semiparametric mixture models and repeated measures: the multinomial cut point model. J R Stat Soc Ser C. 2004;53(3):463–474.
  • Hettmansperger TP, Thomas H. Almost nonparametric inference for repeated measures in mixture models. J R Stat Soc Ser B. 2000;62(4):811–825.
  • Bordes L, Mottelet S, Vandekerkhove P. Semiparametric estimation of a two-component mixture model. Ann Stat. 2006;34(3):1204–1232.
  • Bonhomme S, Jochmans K, Robin JM. Nonparametric estimation of finite mixtures from repeated measurements. J R Stat Soc Ser B. 2014;78:211–229.
  • Doo W, Kim H. Bayesian variable selection in clustering high-dimensional data via a mixture of finite mixtures. J Stat Comput Simul. 2021;91(12):2551–2568.
  • Leung DHY, Qin J. Semi-parametric inference in a bivariate (multivariate) mixture model. Stat Sin. 2006;16:153–163.
  • Simola U, Cisewski-Kehe J, Wolpert RL. Approximate Bayesian computation for finite mixture models. J Stat Comput Simul. 2021;91(6):1155–1174.
  • Silverman BW. Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. Ann Stat. 1978;6(1):177–184.
  • Bowman AW, Azzalini A. Applied smoothing techniques for data analysis. New York: Oxford University Press; 1997.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.