Maximum Likelihood With a Time Varying Parameter

Alberto Lanconelli () and Christopher S. A. Lauria ()
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Alberto Lanconelli: Università di Bologna
Christopher S. A. Lauria: Università di Bologna

Statistical Papers, 2024, vol. 65, issue 4, No 24, 2555-2566

Abstract: 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.

Keywords: Stochastic gradient descent; Maxim likelihood; Exponential family; 65K05; 62F12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01497-y

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