Elements of Large-Sample Theory (Springer Texts in Statistics) by E.L. Lehmann | (PDF) Free Download

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Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

User’s Reviews

Editorial Reviews: Review From a review:EUROPEAN MATHEMATICAL SOCIETY”The book also contains rich collection of problems and a useful list of references, and can be warmly recommended as a complementary text to lectures on mathematical statistics, as well as a textbook for more advanced courses.” About the Author E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: E.L. Lehmann and George Casella, Theory at Point Estimation, Second Edition. Springer-Verlag New York, Inc., 1998, 640 pp., Cloth, ISBN 0-387-98502-6. E.L. Lehmann, Testing Statistical Hypotheses, Second Edition. Springer -Verlag New York, Inc., 1997, 624 pp., Cloth, ISBN 0-387-94919-4.

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

⭐this is an excellent book, you learn all you need to know for large sample theory from a practical perspective (either to apply it or write your own paper using the results). All chapters except chapter 6 (I recommend to skip it all together) are excellent in exposition of the subject. Lehman proceeds with both theoretical results and lots of examples.The 2nd chapter is very fundamental for the rest of the book, all the notions of “probability in law”, “convergence in Probability”, central limit theorem in all its forms (iid, dependent variables) are given. Chapters 3 and 4 are little technical in nature, Chapter 3 deals with performance tests, power of a test, efficiency of test, and chapter 4 with estimation. Chapter 5 deals with extension of the theory to bivariate and multivariate. Lehman’s exposition of the subject in this chapter is phenomenal (not the dry approach I usually see in other books where formulas are just been stated). Many practical theoretical results are been proven, and you get to see the big picture. Chapter 7 that deals with maximum likelihood is also excellent in exposition. Proves theorems for one and multi-parameter case, and efficiency of estimators. The whole chapter until the last page is a gem.PS Chapter 6 for non-parametric estimation did not like at all. The first section is missing information that will enable you to derive the statements in the section for U-statistics. ( I had to read the lecture notes by Ferguson at UCLA and Bartlett’s notes at Berkeley to figure out the statements). The other sections (on statistical functionals and bootstrapping) did not have the same problem, but I found their content of little practical significance.

⭐This is a good book on large sample theory with lots of examples and background material. It is suitable for graduate level or researchers trying to get to grips with this tricky topic. That said, more computing based examples incluing code showing the actual mechanics involved and graphical results would help or consistency proofs as well as graphics sowing convergence of a squence of distributions to the asymptotic distribution would be useful.

⭐Good. It is just as I expected. Good. It is just as I expected. Good. It is just as I expected.

⭐This is one of my favorite books in statistics. I work in the applied sciences, and therefore my review may not necessarily reflect the view of a person looking at this subject purely for its mathematical beauty. This book does a wonderful job explaining how much symmetry there is in the world and do what you will, you mostly end up with a normal distribution in some form or the other in the large sample limit.I feel that a lot of the books on large sample theory, since they are geared towards mathematicians tend to be biased by the counter-examples one encounters in the corner of the parameter space. This book does mention quite a few of these counter-examples, but makes sure to emphasize the abundance and diversity of cases in which the results are `well behaved and smooth’ in the interior; I failed to fully appreciate the latter point in the shorter, more terse texts. In a lot of the problems I work on in demography (and I am guessing in a lot of other areas too), it is quite a non-issue to assume the parameter is bounded away from the corner, and therefore the corner issues become irrelevant.A good analogy to the problem is one of different groups of people looking at a smooth cup with a jagged edge. I say `Wow, look how smooth the cup is, isn’t it awesome?’ and the mathematician says `Yes, but look how jagged the edge is! isn’t that more awesome?’, so I guess it is a matter of taste.Although this book is amazing for learning, it can be a little difficult to use as a reference. For instance, key properties of a test described in chapter 2 might be derived in chapter 4 (because the relevant concept is covered there). This can be frustrating because a lot of back and forth has to be done to refresh ones memory. (I recommend `Asymptotic Statistics’ by Arinban DasGupta as a reference book; several small chapters, dense with information but probably not as good for learning). I don’t think this minor grievance can be held against Dr. Lehmann’s book, since it is designed more as a course text than as a reference.Overall, I would say if a person has done a first course in statistics this is definitely the way to go; working through this book pays rich dividends, and you suddenly start seeing normals in everything: the `Central Limit Theorem’ is central indeed !

⭐Erich Lehmann is well known for his advanced statistical texts on hypothesis testing and estimation. he has also written a nice intermediate level text on nonparametric methods based on ranks. This book is another advanced text providing a thorough treatment of asymptotic (large sample theory) methods. It is very modern and includes such popular current topics as bootstrap and density estimation.

⭐A very good textbook which I needed to get hold of for a uni unit I am studying. It’s a bit abstract in places but worth it, very interesting reading from an experienced statistician. It came a lot quicker than I expected too, in just over 1 week, compared to 4-6 weeks which various bookshops told me I’d have to wait. Great effort Amazon!

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