Good Book on Mathematical Statistics

I'm a mostly self-trained analyst with degrees in the social sciences but not in statistics. I'm looking to improve my knowledge of the mathematics underlying various statistical techniques, but have struck out searching out good books on mathematical statistics for self-study.

Most of the books I've found are either way too basic (explaining random sampling, frequency tables and crosstabs, and ending with linear regression) or are 700 page long textbooks that cost hundreds of dollars and are not very readable.

Can anyone recommend a good book on mathematical statistics for self-study? Maybe something from the Dover math series that is relatively brief, readable, and inexpensive?


Super Moderator
in my opinion, the best book there is for Mathematical Statistics is the classic of classics Casella & Berger. maybe you can buy it used or just borrow it from your library? i think actually most people who did their undergrad in math/stats either used this book or are at least familiar w/ it.

how familiar are you with calculus and linear algebra?


Super Moderator
well, it's a classic so i'd assume you can take it out of any library? plus i don't think you can find any short books that dwell on the mathematical underpinnings of statistical methods. unless you're willing to get one book at a time that deals with one method at a time, maybe?


Ambassador to the humans
I second the recommendation for Casella & Berger. I'm a grad student in statistics and it's the best book I've come across - end of story. It's worth the money but if you want to check it out before purchasing you could try to find a pdf version floating around somewhere....
The book from Casella and Berger is indeed a good book on the mentioned topic.

Anyway my advice would be

Shao, J. (2003). Mathematical Statistics. Springer

combined with

Shao, J. (2005). Mathematical Statistics: Exercises and Solutions. Springer