Numerical methods for nonlinear estimating equations

Hardcover | February 3, 2004

byChristopher G. Small, Jinfang Wang

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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, and the use of root search algorithms, or one-stepestimators, is a standard method 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 nonconcavityoften have very poor convergence properties, and for additional flexibility proposes a numberof modifications to the standard methods for solving these algorithms. The book also extends 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. Avariety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specificallyoriginal. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user'sperspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjortand Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction

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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, and the use of root search algorithms, or one-stepestimators, is a standard method of solution. ...

Christopher G. Small is a Professor of Statistics at the University of Waterloo, Canada, and has been Canada's official representative and Team Leader for the International Mathematical Olympiad in Taiwan (1998) and Washington (2000). Jinfang Wang is an Associate Professor in Obihiro University.

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Format:HardcoverDimensions:322 pages, 9.21 × 6.14 × 0.84 inPublished:February 3, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506880

ISBN - 13:9780198506881

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Table of Contents

IntroductionEstimating functionsNumerical algorithmsWorking with rootsMethodologies for root selectionArtificial likelihoods and estimating functionsRoot selection and dynamical systemsBayesian estimating functionsBibliographyIndex