I am looking for an advanced introduction to statistics. I am currently interviewing for hedge fund positions, and a solid base in statistics would be quite helpful. As a math major I have significant (graduate level) background in analysis and probability, but somehow statistics has always evaded my course schedule. An ideal book would include several proofs in the exposition and a multitude of computational exercises.
I think that "An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)" suggested by KarolisR could be useful but too much machine learning oriented. Moreover, such a book is for beginners.
As a thorough book (PhD level) on statistics, I suggest "Statistical Inference" by Casella and Berger.
You could try this one: An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics). Or maybe take a stats course on coursera/edx
Advanced Algorithmic Trading, Mike Halls-Moore.