Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling.
In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.
1. Introduction ; 2. Elements of likelihood inference ; 3. More properties of the likelihood ; 4. Basic models and simple applications ; 5. Frequentist properties ; 6. Modelling relationships: regression models ; 7. Evidence and the likelihood principle ; 8. Score function and Fisher information ; 9. Large Sample Results ; 10. Dealing with nuisance parameters ; 11. Complex data structure ; 12. EM Algorithm ; 13. Robustness of likelihood specification ; 14. Estimating equation and quasi-likelihood ; 15. Empirical likelihood ; 16. Likelihood of random parameters ; 17. Random and mixed effects models ; 18. Nonparametric smoothing