Title Numerical methods for nonlinear estimating equations / Christopher G. Small, Jinfang Wang

Published Oxford : Clarendon Press ; New York : Oxford University Press, 2003

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Description 1 online resource (xii, 309 pages) : illustrations Series Oxford statistical science series ; 29 Oxford statistical science series ; 29. Contents Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Background to the problem; 1.2 Organisation of the book; 2 Estimating functions; 2.1 Basic definitions; 2.2 Godambe efficiency: one-parameter models; 2.3 The score function: one-parameter models; 2.4 Godambe efficiency: multiparameter models; 2.5 A geometric interpretation of Godambe efficiency; 2.6 Types of estimating functions; 2.6.1 Quasi-likelihood and semi-parametric models; 2.6.2 Martingale estimating functions; 2.6.3 Empirical characteristic functions and stable laws; 2.6.4 Quadrat sampling; 2.7 Bibliographical notes 3 Numerical algorithms3.1 Introduction; 3.2 The bisection method; 3.3 The method of false positions; 3.4 Muller's method; 3.5 Iterative substitution and the contractive maps; 3.6 Newton-Raphson and its generalisations; 3.6.1 Newton-Raphson as a substitution algorithm; 3.6.2 Quasi-Newton algorithms; 3.7 The E-M algorithm; 3.7.1 The E-M algorithm for likelihood equations; 3.7.2 The E-M algorithm for other estimating equations; 3.8 Aitken acceleration of slow algorithms; 3.9 Bernoulli's method and the quotient-difference algorithm; 3.10 Sturm's method; 3.11 Roots and eigenvalues 3.12 The Nelder-Mead algorithm3.13 Jacobi iteration for quasi-likelihood; 3.14 Bibliographical notes; 4 Working with roots; 4.1 Introduction; 4.2 Non-identifiable parameters in mixture models; 4.3 Estimation of the correlation coefficient; 4.4 The Cauchy distribution and stable laws; 4.5 The relative likelihood principle; 4.6 Estimating the normal mean in stratified sampling; 4.7 Regression with measurement error; 4.8 Weighted likelihood equations; 4.9 Detecting multiple roots; 4.10 Finding all the roots; 4.11 Root functionals and measures; 4.12 Smoothing the likelihood function 5.9 Testing the consistency of roots5.10 Bootstrap quadratic likelihood ratio tests; 5.10.1 Bootstrap quadratic likelihood; 5.10.2 Bootstrap quadratic likelihood ratio test; 5.10.3 Example: Cauchy location-model; 5.10.4 Example: logistic regression with measurement errors; 5.11 An information theoretic approach; 5.12 Model enlargement; 5.12.1 Introduction; 5.12.2 Model embedding via mixing; 5.12.3 Examples; 5.13 Non-existence of roots; 5.14 Confidence intervals using the estimating function bootstrap; 5.14.1 Introduction; 5.14.2 Bootstrap-t intervals; 5.14.3 The estimating function bootstrap Summary This text provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It contains extensive coverage and comparison of hill climbing algorithms, which, when started at points of nonconcavity often have very poor convergence properties Bibliography Includes bibliographical references (pages 287-295) and index Notes English Subject Generalized estimating equations. Numerical analysis. MATHEMATICS -- Probability & Statistics -- General. Generalized estimating equations Numerical analysis Form Electronic book Author Wang, Jinfang, author. ISBN 0198506880 9780198506881 9780191545092 0191545090 9780191709258 0191709255

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