Stella & Rose's Books

Front cover

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
• 2.7 Bibliographical notes
• 3 Numerical algorithms
• 3.1 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
• 3.7 The E-M algorithm
• 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 algorithm
• 3.13 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 questions
• 4.9 Detecting multiple roots
• 4.10 Finding all the roots
• 4.11 Root functionals and measures
• 4.12 Smoothing the likelihood function
• 5 Methodologies for root selection
• 5.1 Introduction
• 5.2 The problem of solving an estimating equation
• 5.3 A class of irregular estimating functions
• 5.4 Iterating from consistent estimators
• 5.5 A modified Newton's method
• 5.6 An algorithm based on the information identity
• 5.7 A modified Muller's method
• 5.8 Asymptotic examinations
• 5.9 Testing the consistency of roots
• 5.10 Bootstrap quadratic likelihood ratio tests
• 5.11 An information theoretic approach
• 5.12 Model enlargement
• 5.13 Non-existence of roots
• 5.14 Confidence intervals using the estimating function bootstrap
• 5.15 Bibliographical notes
• 6 Artificial likelihoods and estimating functions
• 6.1 Introduction
• 6.2 Projected likelihoods
• 6.3 Generalised projected artificial likelihoods
• 6.4 Artificial likelihoods through integration
• 6.5 Quadratic artificial likelihoods
• 6.6 Quadratic inference functions
• 6.7 Bibliographical notes
• 7 Roots selection and dynamical systems
• 7.1 Dynamical estimating systems
• 7.2 Linear dynamical systems
• 7.3 Stability of roots to estimating quotations
• 7.4 A modified Newton's method
• 7.5 Complex estimating functions and Julia sets
• 8 Baesian estimating functions
• 8.1 Introduction
• 8.2 Bayes consistency
• 8.3 A Bayesian approach to estimating functions
• 8.4 Bayes linear and semi-parametric estimation
• 8.5 An application to credibility estimation in actuarial science
• 8.6 Bibliographical notes
• Bibliography
• Index