I'm interested on acquiring a strong foundation in statistics. I have just finished Introduction to Probability by Joe Blitzstein and I'm looking for a good book on statistics before moving to The Elements of Statistical Learning.

I have searched through many posts across this site and I'm not sure about which book to pick in order to do so. I'm between Casella and Berger Statistical Inference and Wasserman All of Statistics. Since my mid term goal is research, maybe Casella and Berger would be a better choise, since seems more in depth and focused to traditional statistics, but I'm not sure.

Which one would you recommend me?

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    $\begingroup$ All of Statistics is easier to read but Statistical Inference is deeper and more rigorous. So it is up to you to choose which features are more important to you. $\endgroup$ – Michael Chernick Jun 25 '18 at 19:46
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    $\begingroup$ Casella & Berger is a very standard text for a first course in mathematical statistics. I haven't read All of Statistics, but you might find that since a large portion of Casella & Berger is focused on lots of technical details (e.g. Basu's theorem) that you might not find a whole lot in C&B which is directly related to ESL. $\endgroup$ – Sycorax Jun 25 '18 at 20:02

May I suggest using Larry Wasserman's LN that are available on: http://www.stat.cmu.edu/~larry/=stat705/?

Although Larry has removed the homeworks (and solutions), the LNs are very well written. A big bonus is the link to Larry's videos posted on YouTube. Unfortunately, the video quality is not that great but Larry is an amazing lecturer. I audited (in-class) an earlier version of Larry's course ...

Given CMUs machine learning focus, Larry's course design is to prepare students for graduate-level machine learning courses. So, Larry will spend more time on topics that fulfill that goal (cf. traditional intermediate statistics texts).


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