Maximum Likelihood With a Time Varying Parameter

• URL: http://arxiv.org/abs/2302.14529v1
• Date: Tue, 28 Feb 2023 12:40:42 GMT
• Title: Maximum Likelihood With a Time Varying Parameter
• Authors: Alberto Lanconelli and Christopher S. A. Lauria
• Abstract summary: We consider the problem of tracking an unknown time varying parameter that characterizes the evolution of a sequence of independent observations. We propose a gradient descent-based scheme in which the log-likelihood of the observations acts as time varying gain function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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