Likelihood Methods in Statistics [Hardcover]

This book provides an introduction to the modern theory of likelihood-based statistical inference. This theory is characterized by several important features. One is the recognition that it is desirable to condition on relevant ancillary statistics. Another is that probability approximations are based on saddlepoint and closely related approximations that generally have very high accuracy. A third aspect is that, for models with nuisance parameters, inference is often based on marginal or conditional likelihoods, or approximations to these likelihoods. These methods have been shown often to yield substantial improvements over classical methods. The book also provide an up-to-date account of recent results in the field, which has been undergoing rapid development.

1. Some basic concepts
2. Large-sample approximations
3. Likelihood
4. First-order asymptotic theory
5. Higher-order asymptotic theory
6. Asymptotic theory and conditional inference
7. The signed likelihood ratio statistic
8. Likelihood functions for a parameter of interest
9. The modified profile likelihood function
Appendix: Data sets used in the examples
References
Author index
Subject index

This book presents an excellent overview of modern likelihood methods. The presentation is clear and readable enough to be of considerable use to intermediate level graduate students, but is complete and up-to-date enough to act as an excellent first reference for beginning researchers in the field. . . . Moreover, there are excellent discussions of important references as well as numerous exercises. . . . The field of likelihood asymptotics has been undergoing an increasingly rapid development over the last two decades, and this book provides an excellent and detailed account of where the field is, where it came from and perhaps even a bit about where it is going. --Mathematical Reviews