On the maximization of likelihoods belonging to the exponential family using a Levenberg–Marquardt approach

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 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.

KEYWORDS:

• Aitchison distribution
• compositional data
• Dirichlet distribution
• generalized linear models
• natural link
• optimization

AMS SUBJECT CLASSIFICATION:

• 62F10
• 65C60

Disclosure statement

No potential conflict of interest was reported by the authors.