Theoretical grounding for estimation in conditional independence multivariate finite mixture models

Xiaotian Zhu, David R. Hunter

Research output: Contribution to journalArticle

1 Scopus citations


For the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalised smoothed Kullback–Leibler distance. The nonlinearly smoothed majorisation-minimisation (NSMM) algorithm is derived from this perspective. An elegant representation of the NSMM algorithm is obtained using a novel projection-multiplication operator, a more precise monotonicity property of the algorithm is discovered, and the existence of a solution to the main optimisation problem is proved for the first time.

Original languageEnglish (US)
Pages (from-to)683-701
Number of pages19
JournalJournal of Nonparametric Statistics
Issue number4
Publication statusPublished - Oct 1 2016


All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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