On the maximization of likelihoods belonging to the exponential family using ideas related to the Levenberg-Marquardt approach

Marco Giordan; Federico Vaggi; Ron Wehrens

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arXiv · 1410.0793

On the maximization of likelihoods belonging to the exponential family using ideas related to the Levenberg-Marquardt approach

Marco Giordan·Federico Vaggi·Ron Wehrens

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Abstract

The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood problems when the underlying distributions are in the exponential family. We formally demonstrate a local convergence property and we discuss a possible implementation of the penalization involved in this class of algorithms. Applications to real and simulated compositional data show the stability and efficiency of this approach.

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Marco Giordan, Federico Vaggi, Ron Wehrens. 2014-10-03. On the maximization of likelihoods belonging to the exponential family using ideas related to the Levenberg-Marquardt approach. https://arxiv.org/abs/1410.0793

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