Theoretical grounding for estimation in conditional independence multivariate finite mixture models

Xiaotian Zhu, David R. Hunter

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume28
Issue number4
DOIs
StatePublished - Oct 1 2016

Fingerprint

Finite Mixture Models
Conditional Independence
Multiplication Operator
Projection Operator
Nonparametric Estimation
Monotonicity
Objective function
Optimization Problem
Formulation
Conditional independence
Finite mixture models

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Theoretical grounding for estimation in conditional independence multivariate finite mixture models. / Zhu, Xiaotian; Hunter, David R.

In: Journal of Nonparametric Statistics, Vol. 28, No. 4, 01.10.2016, p. 683-701.

Research output: Contribution to journalArticle

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