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Convergence of the EM algorithm for continuous mixing distributions

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  • Chung, Yeojin
  • Lindsay, Bruce G.

Abstract

Beyond the expectation–maximization (EM) algorithm for vector parameters, the EM for an unknown distribution function is often used in mixture models, density estimation, and signal recovery problems. We prove the convergence of the EM in functional spaces and show the EM likelihoods in this space converge to the global maximum.

Suggested Citation

  • Chung, Yeojin & Lindsay, Bruce G., 2015. "Convergence of the EM algorithm for continuous mixing distributions," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 190-195.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:190-195
    DOI: 10.1016/j.spl.2014.09.021
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    References listed on IDEAS

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    1. Laird, Nan M. & Louis, Thomas A., 1991. "Smoothing the non-parametric estimate of a prior distribution by roughening : A computational study," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 27-37, August.
    2. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
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