A Smooth nonparametric estimate of a mixing distribution using mixtures of gaussians

Laurence S. Magder, Scott L. Zeger

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of Gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h. This approach can lead to estimates of many shapes, with smoothness controlled by parameter h. We show that the resulting estimate will always be a finite mixture of Gaussians, each having variance h. The nonparametric maximum likelihood estimate can be viewed as a special case, with h = 0. The method can be extended to estimate multivariate mixing distributions. Examples and the results of a simulation study are presented.

Original languageEnglish (US)
Pages (from-to)1141-1151
Number of pages11
JournalJournal of the American Statistical Association
Volume91
Issue number435
DOIs
StatePublished - Sep 1 1996

Keywords

  • Deconvolution
  • Empirical bayes
  • Longitudinal data
  • Mixed models
  • Mixtures
  • Random effects

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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