@article{Kasahara:273629,
      recid = {273629},
      author = {Kasahara, Hiroyuki and Shimotsu, Katsumi},
      title = {Nonparametric Identification and Estimation of  Multivariate Mixtures},
      address = {2007-12},
      number = {2110-2018-4278},
      series = {Working Paper No. 1153},
      pages = {26},
      year = {2007},
      abstract = {We study nonparametric identifiability of finite mixture  models of k-variate data with M subpopulations, in which  the components of the data vector are independent  conditional on belonging to a subpopulation. We provide a  sufficient condition for nonparametrically identifying M  subpopulations when k  3. Our focus is on the relationship  between the number of values the components of the data  vector can take on, and the number of identifiable  subpopulations. Intuition would suggest that if the data  vector can take many different values, then combining  information from these different values helps  identification. Hall and Zhou (2003) show, however, when k  = 2, two-component finite mixture models are not  nonparametrically identifiable regardless of the number of  the values the data vector can take. When k  3, there  emerges a link between the variation in the data vector,  and the number of identifiable subpopulations: the number  of identifiable subpopulations increases as the data vector  takes on additional (different) values. This points to the  possibility of identifying many components even when k = 3,  if the data vector has a continuously distributed element.  Our identification method is constructive, and leads to an  estimation strategy. It is not as efficient as the MLE, but  can be used as the initial value of the optimization  algorithm in computing the MLE. We also provide a  sufficient condition for identifying the number of  nonparametrically identifiable components, and develop a  method for statistically testing and consistently  estimating the number of nonparametrically identifiable  components. We extend these procedures to develop a test  for the number of components in binomial mixtures.},
      url = {http://ageconsearch.umn.edu/record/273629},
      doi = {https://doi.org/10.22004/ag.econ.273629},
}