Rating: 
Summary: Very good
Review: This is an excellent textbook. It has numerous
examples and very good exercises, and frequently
mentions recent research. (Another reviewer's
suggestion that Hogg & Craig is an alternative
misses the point: the purposes of the two books
are different; this one is more theoretical.)
(I have a qualm: these authors' take on what
fiducial inference is, is strange.)
Rating:
Summary: great introduction to statistical inference
Review: This textbook was a choice for gradute statistical inference course and recommended for the first graduate econometrics course at Yale. It starts with a small chapter on probability, which is very introductory, so you cannot learn something on probability and measure from this book, but it gives a great treatment of statistical inference and it has very nice and readable presentation of material. It covers such concepts as sufficiency, likelihood principle, method of moments estimation, hypothesis testing and decision theory. The only problem with that book is its price. Also I think that the last two chapters on ANOVA and regression could be omitted.
Rating: 
Summary: Excellent introduction to mathematical staticstics, but...
Review: We used this one as text in the senior undergraduate course this semester. This book is an excellent introduction to mathematical statistics but probably too difficult for most undergraduate students to learn in just one semester.In my opinion, to read this book you Do need a strong background in calculus. Having taken courses like real analysis, introductory probability/statistics is helpful but not so necessary. Most difinitions and proofs are clear and precise. The examples are good, but the authors quite often refer to the previous ones, which may be anoying for many readers. The excercises are great but take a lot of time to work out. In my case, each one took me about one hour on average. And I feel that quite some problems require "mathematics" besides knowlege of statistics. I recommend that you solve as many excercises as possible. Our Professor assigned at least 20 from each chapter as homework. One more thing, I bought the first printing of the book, and found quite a few typos. You can download from the author's homepage the errata list but that doesn't cover all. In conclusion if you are a serious math student interested in mathematical statistics, I think this is a good book for you.
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