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The back cover of this book states that this book is for people who want to learn statistics quickly. Before reading this book, I had taken one second-year calculus-based probability course, and one very non-rigorous biostatistics course. As such, I knew nothing of rigorous statistics. I just finished chapter 11. With this in mind, here is a pros and cons list.
Pros: -There is definitely a lot of material. Many reviews say that this book is great as a reference, and I know some stats majors that like it for this reason. -There is no assumed prior knowledge of measure theory, and it isn't required. -When proofs are given, they are usually complete with very few holes to fill. -The book is about 1/4 examples.
Cons: -The material is not very well motivated; we don't really get down to the "why" of all of the statistics. -The book is rife with abuse of notation which is not explicitly introduced. -Definitions are unclear. For example, the author defines the "size alpha Wald test" in such a way that the test is not actually of size alpha (it is asymptotically size alpha). -Many results are stated without proof, even though their proofs are not necessarily difficult, just a bit technical. For example, Neyman-Pearson Lemma is not proven. Moreover, there is often no reference made to other sources should the reader want to see the proof. -Some exercises are not well-posed. -Many topics are rushed, with the applications completely glossed over.
You will learn statistics quickly; you will not learn statistics very well.
This book is great. The overviews of the topics are insightful, but the book can be quite confusing if you do not have a mathematical background. As a social scientist, I tried to use this book to learn statistics. I wished there were more examples.
Comprehensive treatment of the subject, but not rigorous. A professional mathematician would cringe, but a practicing statistician will love the way the book gets at all the core aspects of the subject in a rapid manner.