Book

Numerical Methods for Nonlinear Estimating Equations

Christopher G. Small and Jinfang Wang

Published in print October 2003 | ISBN: 9780198506881
Published online September 2007 | e-ISBN: 9780191709258 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198506881.001.0001

Series: Oxford Statistical Science Series

Numerical Methods for Nonlinear Estimating Equations

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Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators. Root search algorithms and one-step estimators are standard methods of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms which, when started at points of nonconcavity, often have very poor convergence properties. For additional flexibility, number of modifications to the standard methods for solving these algorithms are proposed. The book also goes beyond simple root search algorithms to include a discussion of the testing of roots for consistency and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities.

Keywords: artificial likelihood; Bayesian estimating functions; dynamical system; iterative algorithm; multiple roots; quasi-likelihood; root selection; semiparametric model; statistical inference

Book.  322 pages.  Illustrated.

Subjects: Probability and Statistics

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Table of Contents

Introduction in Numerical Methods for Nonlinear Estimating Equations

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Estimating functions in Numerical Methods for Nonlinear Estimating Equations

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Numerical algorithms in Numerical Methods for Nonlinear Estimating Equations

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Working with roots in Numerical Methods for Nonlinear Estimating Equations

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Methodologies for root selection in Numerical Methods for Nonlinear Estimating Equations

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Artificial likelihoods and estimating functions in Numerical Methods for Nonlinear Estimating Equations

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Root selection and dynamical systems in Numerical Methods for Nonlinear Estimating Equations

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Bayesian estimating functions in Numerical Methods for Nonlinear Estimating Equations

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