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Nonparametric inference in multivariate mixtures

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  • Peter Hall
  • Amnon Neeman
  • Reza Pakyari
  • Ryan Elmore
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    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.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 92 (2005)
    Issue (Month): 3 (September)
    Pages: 667-678

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    Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:667-678

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    Cited by:
    1. St├ęphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Sciences Po Economics Discussion Papers 2013-09, Sciences Po Departement of Economics.
    2. 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.
    3. Kasahara Hiroyuki & Shimotsu Katsumi, 2012. "Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures," Global COE Hi-Stat Discussion Paper Series gd12-247, Institute of Economic Research, Hitotsubashi University.
    4. Hiroyuki Kasahara & Katsumi Shimotsu, 2007. "Nonparametric Identification and Estimation of Multivariate Mixtures," Working Papers 1153, Queen's University, Department of Economics.
    5. 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.
    6. Stephane 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.
    7. Stephane 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.

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