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Maximum Likelihood With a Time Varying Parameter

Author

Listed:
  • Alberto Lanconelli

    (Università di Bologna)

  • Christopher S. A. Lauria

    (Università di Bologna)

Abstract

We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family.

Suggested Citation

  • Alberto Lanconelli & Christopher S. A. Lauria, 2024. "Maximum Likelihood With a Time Varying Parameter," Statistical Papers, Springer, vol. 65(4), pages 2555-2566, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01497-y
    DOI: 10.1007/s00362-023-01497-y
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    References listed on IDEAS

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    1. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
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