This category is all about covering statistical material from earlier courses from a more advanced perspective on probability. There are some new ideas, but mostly what you will get is a deeper understanding of the statistical techniques you already know.
- In-text exercises
- Solution manual available
Shao's text is a good option for mathematical statistics (admittedly, there aren't many options). It has a sufficient primer on measure-theoretic probability such that you don't really need to have studied it before. We think you should though, as it takes some time to come to terms with advanced probability. Most of Shao's book is devoted to defining classical statistical methods from a measure-theoretic perspective, although there are some sections on the bootstrap and other nonparametric models. The book is very much in the pure math, definition, theorem, corollary style, so only buy this book if you are mathematically inclined. The best part about this book is that there is an extensive solution manual with hundreds of solved problems from the text. The problems are tough, so that is a great resource.