Introduction to Mathematical Statistics gives you comprehensive coverage with a proven approach, promoting understanding with numerous illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and its flexible organization makes it ideal for a range of mathematical statistics courses. In the 8th Edition, substantial revisions help you appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented. Use of statistical software R is expanded throughout. Many additional real data sets illustrate statistical methods or compare methods, and are also available in the free R package hmcpkg. Several important topics have been added including Tukey's multiple comparison procedure in Chapter 9, confidence intervals for the correlation coefficients found in Chapters 9 and 10, and much more
I own both the 5th and 8th editions, and each has their own merits.
I had used the 5th edition when I was first studying the material and find myself returning to it again and again because of its excellent exposition. The authors do a great job of walking the reader through the material, developing the ideas gradually and helping you discover the theory alongside them. It places real emphasis on intuition and understanding, rather than just formalism, which makes it an incredibly enjoyable read. It is easily one of the best math textbooks I have come across, making it a personal favorite.
The 8th edition, on the other hand, I mostly use as a reference book. It is very comprehensive and much more detailed, covering not only the classical foundations of mathematical statistics but also more modern topics. The notation and overall mathematical presentation are much more formal, a noticeable shift away from exposition the earlier edition. Because of this, i think it is best suited for readers who are already comfortable with the subject and know what they are working with, or for the more technical and formally inclined reader.
Very clear and easy to read. Really great if you are transitioning from pure math to industry and are looking for something that is easy and quick to read.