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我以前写的一篇英文心得，发上来和大家分享一下:) 提到的书能下载的应该版上都发过的，大家有兴趣的话搜一下就应该能找到了，呵呵。
There are several levels of statistics which may fit different kinds of researchers.
1. Undergraduate level mathematical statistics
Usually, undergraduate level math statistics is focusing on the introduction of concepts.
For an intermediate level introduction of mathematical statistics, you can refer to the book
(1) Introduction to Probability and Mathematical Statistics (Duxbury Classic) by Lee J. Bain and Max Engelhardt
This is the book I used when I took an undergraduate level statistics. It is very clear and does not lose any rigor. It introduces most important basic concepts in mathematical statistics.
A more advanced level undergraduate book is:
(2) Probability and Statistics, 3rd Edition by Morris H. DeGroot and Mark J. Schervish.
This book is a little bit more difficult to read. It contains more interesting examples and analysis. In fact, it is the textbook used in MIT for undergrads in Math department. If you are interested in it, please refer to the link:
http://ocw.mit.edu/OcwWeb/Mathematics/18-05Spring-2005/CourseHome/index.htm
2. Books between undergraduate level and graduate level:
Books in this level are usually for first year graduate student in applied areas. They are not for Math or Stat students.
(3) Statistics and Data Analysis: From Elementary to Intermediate (SDA) by Ajit C. Tamhane and Dorothy D. Dunlop
It is an excellent book written by one professor in dept. of IEMS, Northwestern University. It contains most techniques in applied statistics. It is textbook when I took IEMS 401 Intermediate statistics last fall. In fact, it is used as the text book for the course applied statistics in Sloan school of management, MIT. For more information, please refer to the link:
http://ocw.mit.edu/courses/sloan-school-of-management/15-075-applied-statistics-spring-2003/index.htm
Note: You can buy a revised edition in China.
(4) Introduction to Mathematical Statistics by Robert V. Hogg, Allen Craig, and Joseph W. McKean, 6th edition.
I just reviewed this book a little bit. It seems that it is a very popular book (please refer to the customer evaluations in Amazon to see some comments). This is the textbook used for IEMS 401 this fall. Also, I find that it is one important reference books in some economics department in US.
Note: You can download the 4th edition from the internet.
3. Books in graduate level (Applied)
(5) Statistical Inference by George Casella and Roger L. Berger, 2nd edition.
Standard text for first year graduate student. The most important advantage of this book is that it does not depend on Measure theoretical probability. That is to say; you can grasp it if you have taken an undergraduate level probability and statistics course. It is the textbook used in dept. of statistics in University of Chicago. On the other hand, it is a very important statistics book used in most economics department. In MIT. it is one of the two textbooks for the course 14.381. Statistical Method in Economics. (Another is the econometrics book by Greene). 14.381 is the required prerequisite for most advanced econometrics courses. For more information, please refer to the link:
http://ocw.mit.edu/courses/economics/14-381-statistical-method-in-economics-fall-2006/index.htm
Note: You can buy a photoprint copy in China. You can also download a scanned version from internet; but the quality is very bad.
4. Book in graduate level (theoretical)
(6) Mathematical Statistics by Jun Shao, 2nd edition
(7) Mathematical Statistics, Updated Printing (2nd Edition) by Peter J. Bickel and Kjell A. Doksum
Thesetwo books are advance theoretical statistics books. It requires somebackground in theoretical probability. However, it can give us a deeperunderstanding in theoretical statistics. In fact, it is used in manytop statistics department.
Prof. Jun Shao is teaching mathematicalstatistics in University of Wisconsin Madison this fall. He gives somelecture notes which may be very helpful if you want to read his book. Please refer to the link:
http://www.stat.wisc.edu/~shao/stat709/main.html
(7) is used in Berkeley. For a brief review of the course, please refer to the link:
http://www.stat.berkeley.edu/~nolan/stat210a/index.html
Note: You can download (6) and (7) from internet. However, the quality of the scanned version of (7) is very bad.
(8) Theory of Point Estimation (Springer Texts in Statistics) by E.L. Lehmann and George Casella, 2nd edition.
(9) Testing Statistical Hypotheses (Springer Texts in Statistics) by E.L. Lehmann and Joseph P. Romano, 3rd edition
(10) Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics) by A. W. van der Vaart
(11) Elements of Large-Sample Theory (Springer Texts in Statistics) by E.L. Lehmann, corrected edition
These4 books are quite advanced. You need a solid background in theoretical probability to read them. In fact, (8)-(10) are used as the textbooksin Stanford. It is a sequence of theoretical statistics courses for a year (three quarters).
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