Numerical Methods for Nonlinear Estimating Equations
Christopher G. Small and Jinfang Wang
Abstract
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 converg ... More
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
Bibliographic Information
| Print publication date: 2003 |
Print ISBN-13: 9780198506881 |
| Published to Oxford Scholarship Online: September 2007 |
DOI:10.1093/acprof:oso/9780198506881.001.0001 |
Authors
Affiliations are at time of print publication.
Christopher G. Small, author
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada
Jinfang Wang, author
School of Agriculture, Obihiro University of Agriculture and Veterinary Medicine, Inada-cho, Obihiro, Hokkaido, Japan
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