On the maximization of likelihoods belonging to the exponential family using a Levenberg–Marquardt approach. Issue 5 (24th March 2017)

• Record Type: Journal Article
• Authors: Giordan, M.; Vaggi, F.; Wehrens, R.
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 5(2017)
• Page Start: 895
• Page End: 907
• Publication Date: 2017-03-24
• Subjects: Aitchison distribution -- compositional data -- Dirichlet distribution -- generalized linear models -- natural link -- optimization; 62F10 -- 65C60; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1238086
• Languages: English
• ISSNs: 0094-9655

Abstract

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.