Nonparametric Identification and Estimation of the Number of Components in Multivariate Mixtures
This article analyzes the identifiability of the number of components in k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k>=2, a lower bound on the number of components (M) is nonparametrically identifiable from the rank of a matrix constructed from the distribution function of the observed variables. Building on this identification condition, we develop a procedure to consistently estimate a lower bound on the number of components.
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- T. P. Hettmansperger & Hoben Thomas, 2000. "Almost nonparametric inference for repeated measures in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 811-825.
- Richard Paap & Frank Kleibergen, 2004.
"Generalized Reduced Rank Tests using the Singular Value Decomposition,"
Econometric Society 2004 Australasian Meetings
195, Econometric Society.
- Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
- Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- I. R. Cruz-Medina & T. P. Hettmansperger & H. Thomas, 2004. "Semiparametric mixture models and repeated measures: the multinomial cut point model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 463-474.
- Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, 01.
- Dunson, David B. & Xing, Chuanhua, 2009. "Nonparametric Bayes Modeling of Multivariate Categorical Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1042-1051.
- Woo, Mi-Ja & Sriram, T.N., 2006. "Robust Estimation of Mixture Complexity," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1475-1486, December.
- Donald W.K. Andrews, 1985.
"Asymptotic Results for Generalized Wald Tests,"
Cowles Foundation Discussion Papers
761R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1986.
- Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
- Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
- M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
- Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer, vol. 49(3), pages 359-381, September.
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