Nonparametric Estimation of Multivariate Mixtures

References

• Allman, E., Matias, C., and Rhodes, J. (2009), “Identifiability of Parameters in Latent Structure Models With Many Observed Variables,” The Annals of Statistics, 37, 3099–3132. DOI:10.1214/09-AOS689.
   Web of Science ®Google Scholar
• Amemiya, T. (1985), “Asymptotic Properties of Extremum Estimators” (Chapter 4), in Advanced Econometrics, Cambridge, MA: Harvard University Press, pp. 105–158.
   Google Scholar
• Benaglia, T., Chauveau, D., and Hunter, D. R. (2009), “An EM-Like Algorithm for Semi- and Non-Parametric Estimation in Multivariate Mixtures,” Journal of Computational and Graphical Statistics, 18, 505–526. DOI:10.1198/jcgs.2009.07175.
   Web of Science ®Google Scholar
• Benaglia, T., Chauveau, D., and Hunter, D. R. (2011), “Bandwidth Selection in an EM-Like Algorithm for Nonparametric Multivariate Mixtures,” in Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P. Hettmansperger, Singapore: World Scientific Publishing Co., pp. 15–27.
   Google Scholar
• Benaglia, T., Chauveau, D., Hunter, D., and Young, D. (2009), “mixtools: An R Package for Analyzing Finite Mixture Models,” Journal of Statistical Software, 32, 1–29. DOI:10.18637/jss.v032.i06.
   Web of Science ®Google Scholar
• Blasques, F. (2010), “Identifiable Uniqueness Conditions for a Large Class of Extremum Estimators,” Meteor Research Memorandum, Maastricht University.
   Google Scholar
• Bonhomme, S., Jochmans, K., and Robin, J.-M. (2016), “Estimating Multivariate Latent-Structure Models,” The Annals of Statistics, 44, 540–563. DOI:10.1214/15-AOS1376.
   Web of Science ®Google Scholar
• Chauveau, D., Hunter, D. R., and Levine, M. (2015), “Semi-Parametric Estimation for Conditional Independence Multivariate Finite Mixture Models,” Statistics Surveys, 9, 1–31. DOI:10.1214/15-SS108.
   Web of Science ®Google Scholar
• Domowitz, I., and White, H. (1982), “Misspecified Models With Dependent Observations,” Journal of Econometrics, 20, 35–58. DOI:10.1016/0304-4076(82)90102-6.
   Web of Science ®Google Scholar
• Frank, A., and Asuncion, A. (2010), UCI Machine Learning Repository [http://archive.ics.uci.edu/ml], Irvine, CA: University of California, School of Information and Computer Science, 213.
   Google Scholar
• Hall, P., Neeman, A., Pakyari, R., and Elmore, R. (2005), “Nonparametric Inference in Multivariate Mixtures,” Biometrika, 92, 667–678. DOI:10.1093/biomet/92.3.667.
   Web of Science ®Google Scholar
• Hall, P., and Zhou, X.-H. (2003), “Nonparametric Estimation of Component Distributions in a Multivariate Mixture,” The Annals of Statistics, 31, 201–224. DOI:10.1214/aos/1046294462.
   Web of Science ®Google Scholar
• Haskell, K. H., and Hanson, R. J. (1981), “An Algorithm for Linear Least Squares Problems With Equality and Nonnegativity Constraints,” Mathematical Programming, 21, 98–118. DOI:10.1007/BF01584232.
   Web of Science ®Google Scholar
• Jiang, B., Yang, F., and Zhang, S. (2016), “Tensor and Its Tucker Core: The Invariance Relationships,” arXiv no. 1601.01469.
   Google Scholar
• Kasahara, H., and Shimotsu, K. (2014), “Non-Parametric Identification and Estimation of the Number of Components in Multivariate Mixtures,” Journal of the Royal Statistical Society, Series B, 76, 97–111. DOI:10.1111/rssb.12022.
   Google Scholar
• Kiers, H. A. (2002), “Setting up Alternating Least Squares and Iterative Majorization Algorithms for Solving Various Matrix Optimization Problems,” Computational Statistics & Data Analysis, 41, 157–170. DOI:10.1016/S0167-9473(02)00142-1.
   Web of Science ®Google Scholar
• Kolda, T. G., and Bader, B. W. (2009), “Tensor Decompositions and Applications,” SIAM Review, 51, 455–500. DOI:10.1137/07070111X.
   Web of Science ®Google Scholar
• Levine, M., Hunter, D. R., and Chauveau, D. (2011), “Maximum Smoothed Likelihood for Multivariate Mixtures,” Biometrika, 98, 403–416. DOI:10.1093/biomet/asq079.
   Web of Science ®Google Scholar
• Scott, D. W., and Wand, M. P. (1991), “Feasibility of Multivariate Density Estimates,” Biometrika, 78, 197–205. DOI:10.1093/biomet/78.1.197.
   Web of Science ®Google Scholar
• Sgouritsa, E., Janzing, D., Peters, J., and Schölkopf, B. (2013), “Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders,” arXiv no. 1309.6860.
   Google Scholar
• Sidiropoulos, N. D., and Bro, R. (2000), “On the Uniqueness of Multilinear Decomposition of N-Way Arrays,” Journal of Chemometrics, 14, 229–239. DOI:10.1002/1099-128X(200005/06)14:3<229::AID-CEM587>3.0.CO;2-N.
   Web of Science ®Google Scholar
• Silverman, B. W. (1978), “Weak and Strong Uniform Consistency of the Kernel Estimate of a Density and Its Derivatives,” The Annals of Statistics, 6, 177–184. DOI:10.1214/aos/1176344076.
   Web of Science ®Google Scholar
• Soetaert, K., Van den Meersche, K., and van Oevelen, D. (2009), “limsolve: Solving Linear Inverse Models,” R Package Version 1.
   Google Scholar
• Wand, M. P., and Jones, M. C. (1994), “Multivariate Plug-In Bandwidth Selection,” Computational Statistics, 9, 97–116.
   Web of Science ®Google Scholar
• White, H. (1980), “Nonlinear Regression on Cross-Section Data,” Econometrica, 48, 721–746. DOI:10.2307/1913132.
   Web of Science ®Google Scholar