Mathematical Statistics (Springer Texts in Statistics) 2nd Edition by Jun Shao (PDF)

Description

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. This new edition has been revised and updated and in this fourth printing, errors have been ironed out. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Subsequent chapters contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.

User’s Reviews

Editorial Reviews: Review From the reviews of the second edition:”The second edition of Mathematical Statistics continues to hold its identity among many other available books on mathematical statistics…The revised and updated version remains of high quality, and I recommend it for use as a text or reference book in a graduate statistics program.” Journal of the American Statistical Association, September 2004″The first edition of this book was published in 1999 … . The main changes include addition of new material in Chapter 1, addition and deletion of a number of exercises, addition of two new sub-sections … . The book remains valuable to instructors and graduate students of traditional mathematical statistics courses, specially for its large collection of problems and for its rigourous presentation.” (Arup Bose, Sankhya: The Indian Journal of Statistics, Vol. 65 (3), 2003)”This book is intended for an advanced postgraduate course in Mathematical Statistics, offered in a mathematically rigorous fashion. … in order to get to grips with rigorous mathematical statistics, this is an ideal book. Also, as a reference book, it is ideally suited. … Two particularly attractive features of the book are the large number of exercises at the end of each chapter – well over a hundred in each chapter, and the fact that asymptotic theory is studied throughout the book … .” (Tertius de Wet, SASJ – South African Statistical Journal, March, 2004)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is good but the quality of cover and paper.

⭐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.

⭐If you like statistics from the more mathematical approach, this is a nice purchase.

⭐This is for PhDs in Mathematical Statistics. Not for any people from applied area. So if you are not trained to be mathematician, don’t touch this book. You need advanced calculus, linear algebra, real analysis, mathematical probability knowledge to even start the first page. The author talked about statistical problems as a mathematician. Don’t be confident if all your statistical training is from applied area.

⭐Does anyone receive this book as a corrected fourth printing as described? I received one that is not the corrected printing every time.

⭐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.—————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.

⭐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.

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

⭐自分は大学院の講義でLehmannのTheory of Point Estimationを読みましたが定義や証明が曖昧でわかりにくいと感じていました。その点この本は測度論をもとに書かれた数理統計学のテキストとして厳密に定義がなされ、証明が展開されています。内容としても点推定論から仮説検定論まで書かれていて数理統計学の基礎が網羅されています。英語に抵抗がなく、数学科などで測度論的確率論をすでに学んだ人にとってはこちらのテキストのほうがストレスなく読み進められるのではないかと思います。また別冊でこの本に沿った演習書も出版されているので独学にも向いています。

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