Customer Reviews

Mathematical Statistics: Exercises and Solutions

5 star:		(5)
4 star:		(1)
3 star:		(2)
2 star:		(1)
1 star:		(2)

 

 

This book has all the ingredients of what in my opinion constitutes an excellent mathematics text: rigorous, concise,
self-contained, clear, and taking an abstract point of view. Note however that, due to the latter ingredient, the author studies statistics using a measure-theoretic approach; and thus I highly recommend that a potential reader first study measure theory as a prerequisite. The first chapter reviews the basics of measure theory, but it may seem too giant a first step for some readers.

The first two chapters of the book give a nice overview of probability and statistics, while the remaining chapters expand on three fundamental areas of statistical inference: estimation (both parametric and nonparametric), hypothesis tests, and confidence sets). And I must admit that I'm very impressed with the author! For if a textbook is a reflection of what an author knows about some subject, then Shao represents a treasure trove of knowledge that is so eloquently shared in this book. Anyone serious about doing graduate-level reasearch in statistics should invest a year of studying this book. But be forwarned that most likely one will find this, due to the onslaught of measure theoretic analysis, one of the more challenging books to makes its way on the book shelf. For those who cannot stomach so much analysis, but would like to at least understand the gist of statistics, I recommend Roussas's book of the same title. It is calculus-based and makes some simplifying assumptions (e.g. continuous or discrete) about the distributions, which helps make the math digest easier.

Don't waste your time: this is a rigorous book on mathematical statistics, done right, for mathematically mature readers.

If you want a plug and chug manual, buy something else. If you want precision and rigor, buy this.

Very readible, precise and concise treatment of statistics. Requires mathematical maturity. Although it doesn't require a background in measure theory, some familiarity (or willingness to learn) would be really helpful (Ch. 1 provides an overview of measure-theoretic probability). I read the first half of it in a PhD level statics class. I found its approach refreshing after taking an engineering oriented senior level/grad statistics class. I still frequently consult it.

I don't know if statistics are just that difficult a subject or statistics writers just aren't good. Either way I have not found a satisfactory statistics book that treats the subject rigorously, but still readable. This book is an excellent reference. However, it's notation is cumbersome, if you're not used to it.

Before I started taking the class that uses this book, I took four undergraduate probability and statistics classes, as well as studied advanced topics such as measure theory. That said many of the things in statistics I thought I understood, I found out that I do not, or had a hard time translating my undergraduate knowledge to this level. As with many advanced math subjects, the definitions are not enlightening and no motivation or further discussion is given for most definitions. These definitions are designed to fit into as general theory as possible, but trying to understand why some things are defined the way they were, and what the original intent of the object was, is just not there.

To use this book, you will definitely need the guidance of an expert statistician.

Update: In 2010 I am using this book again to review probability and statistics in preparation for applying to a PhD program in Finance or Risk Management. I still find the book to be extremely clear. Everything still seems up to date, surprisingly. I like that fact this book has a longer useful life than an iPod or a cell phone, but is a LOT cheaper :-). The sections are very concise, sometimes just 2-3 pages, so this is definitely a reference book and not a learning book. I think it's most useful for a quick comparison of the different methods for someone who has already learned most of the material before.
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I know it must be a sign of extreme geekyness to be reviewing statistics books... but it happens to be one of my passions. (So that proves it takes all kinds of people to make the world go around.) I find this book to be unusually clear. Printing is also of high quality and I did not spot sloppy notation errors. I would judge the level to be about first or second year PhD level. First chapter lays out probability theory very well and introduces the more standard notations. I find books that use the less standard notations to be annoying. I got this book to use as a reference book rather than as a textbook. I wanted to have a concise place to look up and compare the different methods. If you are learning this material for the first time, I strongly suggest you take at least one applied statistics course first. I don't think one can learn statistics easily without using data and actually running the models. Also this is definitly a graduate level book. I don't think it will be a good idea to try it before reading through several undergradute-level books on probability, regression, and statistics.

For more descriptive graduate-level books in econometric, "The Practice of Econometrics" by Ernst R. Berndt is good for hands on practice. Kennedy's "A Guide to Econometrics" provides a descriptive explanation of the various models.

This textbook is too technical, even for stat PhD students, and does not introduce many ideas and concepts. However, the biggest problem is that this book is not technically correct. Many proofs pretend to be complete, but actually there are many gaps and many important propositions are left unproved. The book should be honest about what they prove and what they do not prove.

The only advantage of the textbook is clarity in statements, not in proofs. If you want to refer statistical theorems in measure-theoretically sophisticated way, this is a good reference.

This is a pretty technical book on theoretical statistics based on measure-theory. It's very well written. For Ph.D. students or readers with experience in analysis/measure-theory, it's a good investment. For less technical book, I would recommend Casella and Berger's Statistical Inference.

This book, coupled with its accompanying exercises volume is a good source for beginning graduate level statistics.

This is an utterly useless book.

Most of the essential theorems are not proved but left as an exercise to the reader. If the reader already knows how to prove these things, why buy this book.

Stay clear of this book and don't waste your money.

Too many seemingly unrelated topics with little attempt at unification. Equations rather than concepts. No attempt to relate concepts to practical applications. Nothing on the L1 norm. The brief section on permutation tests (and permutation tests applied to ranks) is laughable.

On the plus side, contains many exercises of value to those whose emphasis is on distributions. Good support for the use of the bootstrap in hypothesis testing though no attempt is made to unify or select among the varying approaches to improved CI's.