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Maximum Likelihood Estimation of a General Mixing Distribution: Variations on Parametric Domains

In: Asymptotic and Methodological Statistics

Author

Listed:
  • Ivan Mizera

    (Charles University, Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics)

Abstract

Some plausible, but likely rigorously never investigated properties of the maximum likelihood method for nonparametric estimation of mixing distributions are investigated: in particular, the interplay between the infinite-dimensional functional formulation and finite-dimensional computational renderings. The methodology enables empirical Bayes prediction via nonparametric estimation of the prior (mixing) distribution (so-called g-modeling), in a way proposed already some time ago, and gaining “recent popularity due to Koenker and Mizera’s computational methods”. The setting of the estimation of the mixing distribution in mixture models via maximum likelihood, and its interpretation as a problem of convex optimization with the appropriate dual are introduced. After discussing certain relevant aspects that may not exhibit themselves in typical instances, but still may be important in the abstract setting, a general consistency theorem, utilizing the analytical properties of the parametrically specified mixed distributions, is formulated and proved.

Suggested Citation

  • Ivan Mizera, 2026. "Maximum Likelihood Estimation of a General Mixing Distribution: Variations on Parametric Domains," Springer Books, in: Daniel Hlubinka & Šárka Hudecová & Matúš Maciak & Michal Pešta (ed.), Asymptotic and Methodological Statistics, chapter 0, pages 419-430, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-07178-1_21
    DOI: 10.1007/978-3-032-07178-1_21
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