Implementation in Missing Data Models

  • Christian P. Robert
  • George Casella
Part of the Springer Texts in Statistics book series (STS)

Abstract

Missing data models (introduced in §5.3.1) are a natural application for simulation, since they use it to replace the missing data part so that one can proceed with a “classical” inference on the complete model. However, this idea was slow in being formalized; that is, in going beyond ad hoc solutions with no theoretical justification. It is only with the EM algorithm that Dempster et al. (1977) (see §5.3.3) described a rigorous and general formulation of statistical inference through completion of missing data (by expectation rather than simulation, though). The original algorithm could require a difficult analytic computation for the expectation (E) step and therefore cannot be used in all settings. As mentioned in §5.3.4 and §5.5.1, stochastic versions of EM (Broniatowski et al. 1983, Celeux and Diebolt 1985, 1993, Wei and Tanner 1990b, Qian and Titterington 1991, Lavielle and Moulines 1997) have come closer to simulation goals by replacing the E-step with a simulated completion of missing data (but without preserving the entire range of EM convergence properties).

Keywords

Migration Covariance Income Acidity Convolution 

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Christian P. Robert
    • 1
    • 2
  • George Casella
    • 3
  1. 1.Laboratoire de StatistiqueCREST-INSEEParis Cedex 14France
  2. 2.Dept. de Mathematique UFR des SciencesUniversite de RouenMont Saint Aignan cedexFrance
  3. 3.Biometrics UnitCornell UniversityIthacaUSA

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