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Nonparametric inference in multivariate mixtures

Author

Listed:
  • Peter Hall
  • Amnon Neeman
  • Reza Pakyari
  • Ryan Elmore

Abstract

We consider mixture models in which the components of data vectors from any given subpopulation are statistically independent, or independent in blocks. We argue that if, under this condition of independence, we take a nonparametric view of the problem and allow the number of subpopulations to be quite general, the distributions and mixing proportions can often be estimated root-n consistently. Indeed, we show that, if the data are k-variate and there are p subpopulations, then for each p ⩾ 2 there is a minimal value of k, k-sub-p say, such that the mixture problem is always nonparametrically identifiable, and all distributions and mixture proportions are nonparametrically identifiable when k ⩾ k-sub-p. We treat the case p = 2 in detail, and there we show how to construct explicit distribution, density and mixture-proportion estimators, converging at conventional rates. Other values of p can be addressed using a similar approach, although the methodology becomes rapidly more complex as p increases. Copyright 2005, Oxford University Press.

Suggested Citation

  • Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
  • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:667-678
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    File URL: http://hdl.handle.net/10.1093/biomet/92.3.667
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    Cited by:

    1. Victor Aguirregabiria & Pedro Mira, 2013. "Identification of Games of Incomplete Information with Multiple Equilibria and Common Unobserved Heterogeneity," Working Papers tecipa-474, University of Toronto, Department of Economics.
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2014. "Non-parametric identification and estimation of the number of components in multivariate mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 97-111, January.
    3. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    4. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    5. Hiroyuki Kasahara & Katsumi Shimotsu, 2006. "Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices," Working Papers 1092, Queen's University, Department of Economics.
    6. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Working Papers hal-00972868, HAL.
    7. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric estimation of finite measures," CeMMAP working papers CWP11/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    9. Hiroyuki Kasahara & Katsumi Shimotsu, 2007. "Nonparametric Identification and Estimation of Multivariate Mixtures," Working Papers 1153, Queen's University, Department of Economics.
    10. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. David Balan & Patrick DeGraba & Francine Lafontaine & Patrick McAlvanah & Devesh Raval & David Schmidt, 2015. "Economics at the FTC: Fraud, Mergers and Exclusion," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 47(4), pages 371-398, December.
    12. Chauveau, Didier & Hoang, Vy Thuy Lynh, 2016. "Nonparametric mixture models with conditionally independent multivariate component densities," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 1-16.
    13. Alexander Munteanu & Max Wornowizki, 2016. "Correcting statistical models via empirical distribution functions," Computational Statistics, Springer, vol. 31(2), pages 465-495, June.

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