Statistical Inference

Quibbles apart, Casella & Berger is a demanding but most rewarding and stimulating introduction to (so-called) mathematical statistics, and in particular it is exceptionally dependable and witty. Beginning students may require some complementary material in the form of standard exercises and worked-out examples.


Thoughtful book to learn the basics of statisitcal inference   April 20, 1997
14 out of 14 found this review helpful

I used this text in graduate school at North Carolina State University and I found it to be a unique and thoughtful book to learn the basics of statisitcal inference. From the introduction to basic counting theory to deravation of hypothesis tests and confidence intervals I find myself extending the theories introduced to the problems of understanding and summaring data. I continue to refer this text often


Excellent on introduction to univariate statistics   June 16, 2003
J. Wang (NYC, NY)
64 out of 79 found this review helpful

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"..