I am learning statistical inference by myself, I have skim through a few books like Casella Hoggs and I find it omitted lots of details, for example, they didn't introduce the conditional expectation, so there are only proofs in discrete case about "sufficient statistics " "factoring theorem ", etc. could you recommend me a book for graduates or doctor degree? thanks!
background: I'm a first-year graduate student working on probability.
I think you can try to follow the OCW course:
http://ocw.mit.edu/courses/mathematics/18-466-mathematical-statistics-spring-2003/syllabus/
You are certainly right that most introductory statistics books do not use measure theory rigorously, and it is a bit annoying if you knew it already. But if you go through the proofs in the above notes, you will find most are (in my opinion) abstract nonsense with no examples. So like calculus is more useful than real analysis for engineer majors, introductory statistics (in some sense) is more useful than abstract mathematical statistics. I noticed you already asked on cross-validated, so perhaps no need to compile a separate long list at here. As you can see the subject branches off very quickly and what you are looking for depends a lot on your academic interest.
Enjoy!