Nonparametric inference in multivariate mixtures
AbstractWe 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 InfoArticle provided by Biometrika Trust in its journal Biometrika.
Volume (Year): 92 (2005)
Issue (Month): 3 (September)
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- 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.
- Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Sciences Po Economics Discussion Papers 2013-09, Sciences Po Departement of Economics.
- Hiroyuki Kasahara & Katsumi Shimotsu, 2012.
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CIRJE-F-866, CIRJE, Faculty of Economics, University of Tokyo.
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