There is a lot that is different about this second edition. First, there is a co-author without whose help this revision would not have been possible. Second, we have benefited from countless letters from readers and colleagues who have pointed out errors and omissions and have made valuable suggestions over the past 25 years. These communications make this revision worth the effort. Third, we have tried to update the content of the book while striving to preserve the character and spirit of the first edition.

Here are some of the numerous changes that have been made.

1. The Introduction section has been removed. We have also removed Chapter 14 on sequential statistical inference.
2. Many parts of the book have gone substantial rewriting. For example, Chapter 4 has many changes, such as inclusion of exchangeability. In Chapter 3, an introduction to characteristic functions has been added. In Chapter 5 some new distributions have been added while in Chapter 6 there have been many changes in proofs.
3. The statistical inference part of the book (Chapters 8 to 13) has been updated. Thus in Chapter 8 we have expanded the coverage of invariance and have included discussions of ancillary statistics and conjugate prior distributions.
4. Similar changes have been made in Chapter 9. A new section on locally most powerful tests has been added.
5. Chapter 11 has been greatly revised and a discussion of invariant confidence intervals has been added.
6. Chapter 13 has been completely rewritten in the light of increased emphasis on nonparametric inference. We have expanded the discussion of {/-statistics. Later sections show the connection between commonly used tests and {-statistics.
7. In Chapter 12, the notation has been changed to confirm to the current convention.
8. Many problems and examples have been added.
9. More figures have been added to illustrate examples and proofs.
10. Answers to selected problems have been provided.

We are truly grateful to the readers of the first edition for countless comments and suggestions and hope we will continue to hear from them about this edition.

Special thanks are due Ms. Gillian Murray for her superb word processing of the manuscript, and Dr. Indar Bhatia for figures that appear in the text. Dr. Bhatia spent countless hours preparing the diagrams for publication. We also acknowledge the assistance of Dr. K. Selvavel.