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Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics), by A. W. van der Vaart
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This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
- Sales Rank: #316249 in eBooks
- Published on: 1998-10-13
- Released on: 1998-10-13
- Format: Kindle eBook
Review
'The book is extremely well written and clear ... it is comprehensive and has an abundant supply of worked examples ... anyone who is genuinely interested in learning about some of the recent developments in asymptotic statistics and their potential applications should have a copy of this book.' Biometrics
'I recommend this book to every advanced Master's student, Ph.D. student or researcher in mathematical statistics.' Kwantitatieve methoden
Most helpful customer reviews
12 of 12 people found the following review helpful.
Hidden flaws
By Loren Cobb
On first read-through, I was excited by this book. Enough so that I organized and taught a graduate seminar using it as a text. My experience with the book was less than fully satisfactory, I am sorry to say. The subject matter is important, and van der Vaart's pathway through the material is well conceived, but in the nitty-gritty details there are problems. The all-important Chapters 19-25, on asymptotics in metric spaces, suffers from wild differences in level of exposition, even within individual chapters. Some notations and concepts are left undefined. Most proofs are incomplete sketches, leaving many students confused and bewildered. It takes a lot of mathematical maturity to fully decode what van der Vaart has to say, with the result that his message is often missed or misunderstood. The supplementary notes that I felt required to write ballooned from an initial 10 pages to over 60, and I believe that other, more conscientious professors have written far more. I have no doubt that some of those "supplementary" collections of notes will see their way into print, as textbooks that ultimately do a far better job with this critical material.
25 of 25 people found the following review helpful.
Excellent textbook on asymptotics in statistics
By A Customer
This book covers asymptotics at a level suitable for graduate students in statistics and other disciplines such as economics. It does not really treat time-series issues, but apart from that its coverage is very impressive. It covers M-estimators, efficiency, quantile estimators, semiparametrics, and much more. The writing is remarkably lucid; proofs are succinct but very readable. One feature I particularly liked was a very readable introduction to empirical process theory, which would be a good place to start before tackling the van der Vaart and Wellner's more advanced book.
0 of 0 people found the following review helpful.
Excellent book, but leaves out many finer technical details.
By stat007
It is a great book with excellent coverage of topics, but it does not fill in many crucial and important details - the kind of technical details which is exactly what you are looking for. If you are reading it thoroughly, after a stage you will wonder why the author has left so much unwritten and unclear. You may scratch your head on one single statement for a week or more and start feeling frustrated. One particular example is the treatment of M-estimators in Chapter 5.
But, nevertheless it is still worth reading every bit, because it provides extremely useful results and tools in almost all the areas, which it covers.
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