This is a delightful book! It gives a well-written exposure to inference issues in statistics, very suitable for a first-year graduate course. It contains no introductory chapter(s) on probability theory, like so many other books on this topic. The necessary probability concepts are introduced when needed. While the book is heavily mathematical in places, proofs are given with useful verbal justifications for each step. The authors present the material in a very good pedagogical manner. The examples are excellent, and the exercises are very instructive.
The authors introduce and compare the three main approaches to statistical inference: frequentist, Bayesian and Fisherian. This is done without presenting any obvious preference for any of the three. The book is very much up to date and includes recent developments in the field; not shying away from discussing computational procedures should they be called for.
The chapters take the reader through decision theory, Bayesian methods, hypothesis testing, sufficiency and completeness, two-sided and conditional inference, likelihood theory, higher-order theory, predictive inference and bootstrap methods. These topics can provide good reading, not just for students, but also for professionals who perhaps have not kept up with the field and are in need of a refresher book.
Gudmund R. Iversen received his PhD in statistics from Harvard University and taught statistics for many years at The University of Michigan and Swarthmore College until his retirement.
Preface; Introduction; 1. Decision theory; 2. Bayesian methods; 3. Hypothesis testing; 4. Special models; 5. Sufficiency and completeness; 6. Two-sided tests and conditional inference; 7. Likelihood theory; 8. Higher-order theory; 9. Predictive inference; 10. Bootstrap methods; References; Index.