A linearization procedure and a VDM/ECM algorithm for penalized and constrained nonparametric maximum likelihood estimation for mixture models

Jiping Wang*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations


Suppose independent observations Xi, i = 1, ..., n are observed from a mixture model f (x ; Q) ≡ ∫ f (x ; λ) d Q (λ), where λ is a scalar and Q (λ) is a nondegenerate distribution with an unspecified form. We consider to estimate Q (λ) by nonparametric maximum likelihood (NPML) method under two scenarios: (1) the likelihood is penalized by a functional g (Q); and (2) Q is under a constraint g (Q) = g0. We propose a simple and reliable algorithm termed VDM/ECM for Q-estimation when the likelihood is penalized by a linear functional. We show this algorithm can be applied to a more general situation where the penalty is not linear, but a function of linear functionals by a linearization procedure. The constrained NPMLE can be found by penalizing the quadratic distance

Original languageEnglish (US)
Pages (from-to)2946-2957
Number of pages12
JournalComputational Statistics and Data Analysis
Issue number6
StatePublished - Mar 1 2007



  • Computing algorithm
  • Constrained NPMLE
  • Mixture models
  • Nonparametric maximum likelihood
  • Penalized NPMLE

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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