Statistical Models: Theory and Practice

The late Professor David A. Freedman possessed the rare skill of being at the top of his profession in both theoretical and applied statistics. His introductory text with the simple title "Statistics" has been praised as one of the best ever written. On the other side he could write very deep mathematical books as was demonstrated in his trilogy on Markov processes and diffusions. In the real world he contributed to the application of critical thinking about the pros and cons of statistical models and was steadfast in his position against the adjustment of the decennial US Census even though most prominent statisticians stood on the other side. He did consulting which grounded him into real applications particularly in Econometrics. As a Berkeley professor he collaborated with many of the top theoretical statisticians in the world. Many of which were at Berkeley or Stanford.I concur with the enthusiasm for this book that is shown by the other 4 customer reviews. Persi Diaconis from Stanford was a long-time collaborator with Freedman and the late Erich Lehmann long-time Berkeley colleague. I think the praise for this book shown by them is far more important to hear that some of the nice things I might say.Diaconis: "At last, a second course in statistics that is serious, correct, and interesting. The book teaches regression, causal mdoeling, maximum likelihood, and the bootstrap. Everyone who analyzes real data should read this book."Lehmann: "This book is outstanding for clarity of its thought and writng. It prepares readers for a critical assessment of the technical literature in the social and health sciences, and it provides a welcome antidote to the standard formulaic approach to statistics."Lehmann was a great writer himself and in addition to his research contributions to parametric and nonparametric statistics he presented and extended the Neyman-Pearson theory of hypothesis testing in his first book "Testing Statistical Hypotheses" and its subsequent revisions. With that in mind Lehmann's comments about Freedman's clarity of exposition should be taken very seriously.In addition to covering applications and hitting the mostimportant topics in applied statistics in the eight chapters Freedman reproduces completely articles that applied statistics in the sociology, economics and political science journals. he devotes a complete chapter (Chapter 7) to bootstrap methods form estimating bias and standard errors. As an author of a book on the bootstrap I know how difficult it is to explain the bootstrap in a technically accurate way without pouring on the asymptotic theory that goes away from intuition. Freedman, who was a major contributor to the asymptotic theory of the bootstrap and its application in regression and simultaneous equation models that are so often used in econometrics, uses this knowledge and his gift of writing to present this in a way that I will want to learn to emulate.

If you're a student in math or statistics, the book is a good secondary text but not the best standalone. Written at a semi-rigorous level, it will develop a solid foundation for statistics. Even for machine learning people I would recommend it with the caveat that the applications and real-world examples in the book will probably bore you.If you're in the social and health sciences just make sure that you have the mathematical background necessary. There are lots of proofs given in this book. The exercises often ask you to prove things. The math is not tucked neatly away. You need to be comfortable with basic undergrad linear algebra and probability. Otherwise, save yourself the frustration and don't buy this book just yet!The book also just falls a little flat in some places. Particularly, no derivation for OLS is given and the motivation for the chapter on maximum likelihood is really weak and no discussion of regularity conditions. For other concepts too like bootstrap, I think many other books do a better job at motivating and explaining these concepts.If there's one reason to buy this book, its how much stress freedman places on understanding the limitations of statistics. He's done a great job here. I have great respect for him but its a shame the book just doesn't shine anywhere else and just reads like a typical dry statistics book.

I've done a bit of least squares in basic statistics, but I wanted to learn more. This book got such great reviews that I ordered it. I read the first five chapters. I hate to speak ill of the dead, but really, this is a terrible book. A lot of the book and what the author is trying to teach is embedded in exercises and problems. Unfortunately, the author does not provide answers to these. So the reader without the solutions is forced to skip a lot of material.One of the core features of the book in theory is the discussion of least squares. I found this obscure, at best. The discussion of least squares is in terms of linear algebra, which is great. But the jump is rapid and it is difficult to tie the description back to application. Despite all of the proofs I wanted more detail on the derivation for the least squares equations, but I didn't find it. At least not in a for I could understand.In short, this book is not at all a book for self-study. I suspect that few in the social sciences and even Biology would find this text useful. It's just too obscure. What a disappointment!I'm returning mine to Amazon and looking for a better book on least squares and multiple regression.[December 2012] After writing this review I took an advanced statistics for computational finance at the University of Washington. I now probably know more about the theory of least squares than I might want too. One of the references that I used in the class is  Applied Regression Analysis . While on its way to becoming a "classic" this book proves good coverage of linear regression theory and application.  Linear Models with R  by Julian Faraway is a good companion to Draper and Smith, since it covers how the free R software can be applied.

The genius of this book cannot be overstated. This book supplies the ideas, motivations, and insights at the heart of statistical thinking and removes all of the confusing jargon and technicality that burdens most traditional treatments. Its rigor is in ideas, not the pseudo-rigor of pages of poorly motivated formulas. A more advanced follow up on Freedman's "Statistics", these two books solidify for me Freedman's place as a visionary in exposition.

The book is easy to read and lots of interesting information is contained in between the lines. Ideal for practitioners who need to do statistics in their jobs but would never consider studying mathematics in their youth. The few theorems are given without proofs albeit with good references. Only a master in his subject can write a book which is all of it: correct, clear, useful and entertaining.