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A cyclic algorithm for maximum likelihood estimation using Schur complement
Author(s) -
N'Guessan Assi,
Geraldo Issa Cherif
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1999
Subject(s) - hessian matrix , schur complement , coordinate descent , mathematics , complement (music) , algorithm , mathematical optimization , matrix (chemical analysis) , block (permutation group theory) , schur decomposition , system of linear equations , hessian equation , transformation (genetics) , linear system , descent (aeronautics) , eigenvalues and eigenvectors , partial differential equation , quantum mechanics , complementation , gene , phenotype , materials science , first order partial differential equation , aerospace engineering , mathematical analysis , engineering , composite material , geometry , chemistry , biochemistry , physics
Summary Using the Schur complement of a matrix, we propose a computational framework for performing constrained maximum likelihood estimation in which the unknown parameters can be partitioned into two sets. Under appropriate regularity conditions, the corresponding estimating equations form a non‐linear system of equations with constraints. Solving this system is typically accomplished via methods which require computing or estimating a Hessian matrix. We present an alternative algorithm that solves the constrained non‐linear system in block coordinate descent fashion. An explicit form for the solution is given. The overall algorithm is shown in numerical studies to be faster than standard methods that either compute or approximate the Hessian as well as the classical Nelder–Mead algorithm. We apply our approach to a motivating problem of evaluating the effectiveness of Road Safety Policies. This includes several numerical studies on simulated data. Copyright © 2015 John Wiley & Sons, Ltd.