Statistical Inference 2nd Edition by George Casella (PDF)

Description

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. This book can be used for readers who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

User’s Reviews

Editorial Reviews: Review “Statistical Inference is a delightfully modern text on statistical theory and deserves serious consideration from every teacher of a graduate- or advanced undergraduate-level first course in statistical theory. . . Chapters 1-5 provide plenty of interesting examples illustrating either the basic concepts of probability or the basic techniques of finding distribution. . . The book has unique features [throughout Chapters 6-12] for example, I have never seen in any comparable text such extensive discussion of ancillary statistics [Ch. 6], including Basu’s theorem, dealing with the independence of complete sufficient statistics and ancillary statistics. Basu’s theorem is such a useful tool that it should be available to every graduate student of statistics. . . The derivation of the analysis of variance (ANOVA)F test in Chapter 11 via the union-intersection principle is very nice. . . Chapter 12 contains, in addition to the standard regression model, errors-in-variables models. This topic will be of considerable importance in the years ahead, and the authors should be thanked for giving the reader an introduction to it. . . Another nice feature is the Miscellanea Section at the end of nearly every chapter. This gives the serious student an opportunity to go beyond the basic material of the text and look at some of the more advanced work on the topics, thereby developing a much better feel for the subject.”

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

⭐If you have basic training in calculus, you’ll love this well written, easy-to-follow book. It provides a complete list of theories along with rigorous proofs and comprehensive examples, by which it is almost good for self-study.Comparing with many badly written mathematical books by famous names that gave me terrible experiences, I strongly recommend this book. As I was enjoying reading of this book, my memory constantly went back to the difficult time I had experienced when I tried so hard on Royden’s “Real Analysis” or M. Artin’s “Algebra”. These two are classical math textbooks that are appraised by the majority of mathematicians. But from my observation, quite a few students hate these two books to some extreme, because they are so hard to follow unless you read other textbooks. In my opinion, these “bad” textbooks are good only for those who have already mastered the contents (for example, professors who have been teaching this subject for their entire lives). After completely understood the topics, I found these two books are quite useful as reference books. But still I do not think these two books are good to begin with if the reader knows little about the subjects in the books. As contrary, Casella-Berger’s book is very good for entry-level students. Good knowledge in calculus is sufficient for you to easily follow the topics. Moreover, the content of this book is not simple; it contains almost all aspects of univariate statistics. (many poor calculus books are written in such a way that in order to please the students, the author intentionally omitted some important subjects and/or reduced the level of the contents. By doing so, the author became famous and the book went to best-selling. The students, without any working, are happy to wrongly believe that they know everything while they don’t). “Statistical Inference” is good only because it is carefully written. Casella-Berger are not only outstanding researchers, they are also excellent educators. They know students, they know at what point students would encounter what difficulty and at this point, you definitely will find an appropriate example to help you out. The sharp contrasts between “Statistical Inference” and many “bad” textbooks in mathematics convince me that mathematicians are trying to make our lives more miserable (and this is one of the reasons I lost my interests in mathematics, though I have been good at math) while statisticians are trying to make our lives easier.At the same time of going through “Statistical Inference”, I was also reading Richard Durrett’s “Probability: theory and examples”, a widely used typical textbook in probability for first year PhD student. Compared with majority entry-level PhDs in statistics, my background in mathematics (Lebesgue Measure, Integration and Differentiation) is no weaker, yet I experienced the same hard time as I did in some other math classes. My blame can only go to the bad written textbook, I have to read other textbook to understand the topics, and this is not good for a not-stupid and hard working student. I am always curious that among all the textbooks available, why mathematicians prefer the textbooks that will give students more hard time. For the same topic, using different approaches, students will have different feelings, why can’t the professor pick up the more friendly written books for the sake of student’s easy understanding and their continuing interests in the area?My belief was strengthened after completing the reading of Casella-Berger’s “Statistical Inference” and R. Durrett’s “Probability”, that one must keep away from mathematicians as far as possible since your life will be tough if you are close to them. And as for myself, I won’t do research in probability since the book “Probability” gave me the impression that more mathematicians are involved in the area of probability theory. I’ll go with Casella & Berger, concentrate on the filed of statistical inferences since scientists in this particular field are trying to make our lives better and easier.In conclusion, if you need to learn statistics while having no specific back ground, I strongly recommend Casella Berger’s “Statistical Inference”..

⭐I must disagree with the esteemed formal review of this text. It is decidedly the clear opposite of delightful.Unless you already have an understanding of statistical theory or are required to have this text for your course, I cannot recommend it. While it is theoretical and states in the introduction that only two semesters of calculus is sufficient for using the text, in practice things are quite another matter. There are a few positives. I appreciate that the text offers a breadth of topics not included in many others, and that is a positive aspect of the book. While unhelpful, I enjoy the Sherlock Holmes quotes. The selected font is nice. The tables outline distributions and their attributes are very helpful.As for the shortcomings, I find, as a student new to the field on a theoretical level, there are many.First is the structure of the book, itself: I have never had a math book competing with a novel for size. That is to say, the text is compact and the book small, with implications that you are reading dense paragraphs about both math and theory. This makes the material hard to follow and easy to get lost in.Second, while there are several examples given in the text, none are ever worked out in their entirety, not even as an appendix or supplement. Therefore, the book assumes quite a lot of the reader/student/novice and simply tells you that “simple calculus” or “steps from chapter X” are useful in completing a problem. This is a curious tactic, as those with experience teaching math will know that the best way to learn is to see examples worked out over and over again, with no steps omitted. If a student were to submit for grading the work put forth in the book, points would be lost due to the lack of proper hashing out of the steps. And the only way to learn said steps are by seeing them…in one’s text.Third, the book has a maddening habit of referring the reader to exercises as a means of explanation within the chapter. Another odd choice in teaching mechanisms, considering that if the student knew the concept, he/she would not be reading the book and would not require the practice in the first place.Fourth, the exercises are not organized in any logical fashion. That is to say, when one references a math text, problems sets begin simply so to reinforce the concept and build confidence with the student. Then, more challenging problems are introduced to test the knowledge and skill of the student. This text jumps right to the testing phase of questions without the skill-building set…frustrating for students trying to work out challenging concepts in ways that are generally not intuitive.Fifth, the examples within the text are not written in a fashion that one would experience them in an exam or even in the chapter exercises of this very book! That is to say, no clear question is given at the start of the “example.” Rather, steps are covered without you knowing the true starting point.Sixth, there are no practice problems within the text. This would be helpful.Seventh, it is rare that any of the theoretical concepts are provided context so that you have an idea of what the concept is used for in an applied setting, making the content even more difficult to grasp.Finally, the index is not particularly useful, as it is not very thorough. A student is better off making their own notes with reference pages as they go along, rather than rely on the index, which seems to only cover main topics (oddly enough, already covered in the contents).In summary, studying this book makes me feel as though the student should know statistical theory before they know statistical theory…or know the subject before they find the book in any way useful. The authors do not seem to have a clear goal of whether this book should be used as a reference or teaching tool…and so have created a tome with a confusing combination of aspects of both. I am regularly consulting several books at once (and searching the Internet and consulting professors) in order to make sense of much of the text, further supporting the fact that while this book has breadth, the depth is sadly lacking.While the authors allude to the logic of Sherlock Holmes, the hours I spend squeezing sense out of this book rather calls to mind the nonsensicalness of Lewis Carroll’s “Alice in Wonderland.” Thus, I spend much of my time down the rabbit hole.

⭐I finished the reading of the entire book, and I found it excellent in many respects. The first 5 chapters, I think should be used for a course in probability for all engineering/sciences graduate departments . Chapter 5, where the Sample/t/F/order statistics analyzed is superb. Chapters 1-7 are read easily, but starting chapter 8, the material becomes very difficult (I would say 2-3 times more effort than the previous chapters, especially chapter 8 that treats Hypothesis testing). However, Chapter 8 is very crucial for the 2nd part of the book. The book eases out at chapter 11 and 12 (except the middle 1/3 of chapter 12 about structural relationship model – I could not follow it-). I would recommend the authors for chapter 8 to put Exercises 8.34 and 8.37 right on the main text solved , because they are very critical for the understanding of the chapter.I call the book authoritative, because it brings one to a the level where can read papers on machine learning or statistics without big effort.Having said that, there are some pages/theorems that are not clearly exposed, like:- p 342 Theorem 7.3.17, in the proof, the interchange of Expectations is not clear as to why.-p 434 Theorem 9.2.14, the proof is obscured, strange, because in previous page the proof for continuous distributions is fine.- p 600, Equation 12.4.4 equality in last line is unclear

⭐This book provides an excellent introduction to statistical inference and takes a fairly rigorous approach beginning with set theory and introducing the basic axioms of probability theory before introducing distributions. Despite being aimed at graduate students the prerequisites are fairly modest – the authors suggest a year of calculus plus perhaps some exposure to matrices. The written style is engaging and the authors take the trouble to lead the reader through the development of the material. Again, a pleasant surprise for a book aimed at this audience is that it does not avoid explaining straightforward algebraic manipulations or calculus rules used in the derivations presented – these can often trip up any mortal reader and it is refreshing to have these additional notes so that one is not distracted from the important mathematical point by failing to follow the thread of the argument. There are also copious examples and a huge quantity of exercises (presented without answers).Unfortunately this book is let down by poor printed presentation: my copy features pages with text that is in some places faint and occasional not printed at all; printing is often not aligned with the page with lines running at an angle of several degrees to the page edge, and some pages are not cut from their neighbours. This is a pity as the written content is thoughtfully presented and is otherwise a valuable addition to the bookshelf of many mathematicians, perhaps particularly those with a solid grasp of mathematics but less so a background in statistics.

⭐The production quality is very poor.There is also a piece of black tape covering a notice in the front page, but you can read it from the other side as the paper is so thin. It says this edition is only for sale in India, Pakistan, Bangladesh, Nepal or Sri Lanka.Therefore not sure if it’s legal for this to be sold in the UK.

⭐The book is great, but as stated in an other comment the print quality is really poor. I ordered to get an idea myself. The paper is thin so that the ink from the other side of the page makes it very unpleasant to read. On my copy a small mention at the back was obstructed by a black marker. No need to say I returned the book, it looked really dodgy. It’s a shame to get such poor quality when you make the effort to pay £30 for a book you like, especially when that’s shipped and sold from Amazon.

⭐It is completely unuseable, the binding makes parts unreadable and some pages are upside down (this was the official version sold & fulfilled by amazon so definitely not a counterfeit from a third party seller.

⭐Pages very thin and print faint in places. Good information and useful for academic purposes or self interest

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