Pestman, Wiebe R., Mathematical statistics.Mathematical statistics., de Gruyter Textbook. Berlin: de Gruyter (ISBN 978-3-11-020852-8/hbk; 978-3-11-020853-5/ebook). ix, 597 p. (2009). ZBL1251.62001.
It can't be said to be advanced in that it is intended for undergraduates, but it is written in the style of a book for the mathematically mature. I.E. Definition, Theorem, Proof, Example. It even begins with a brief introduction to measure theory. That's a big improvement over most!