Textbook Recommendation: "π¨ππ ππ πΊπππππππππ" by Larry Wasserman
A good book at the graduate level to learn mathematical statistics
If you are studying mathematical statistics at the graduate level, consider using the book "All of Statisticsβ by Larry Wasserman.
It is explains concepts clearly from first principles in a logical manner.
The writing is efficient, straightforward, and free of verbiage.
It is comprehensive, covering all essential areas of probability, mathematical statistics, and statistical inference.
Beyond mathematical statistics, this book also dives into advanced topics, like causal inference, graphical models, and simulation methods.
The publisher is Springer. If your post-secondary institution has access to Springer's books, then you can access it for free.
Many data scientists have never learned mathematical statistics properly from first principles, yet they use "All of Statistics" to learn this subject for the first time. I do NOT encourage this, even though I like this book a lot.
Previously, I suggested the book "Introduction to Mathematical Statistics" for upper-undergraduate and graduate students. I still urge you to use it as your primary resource for graduate mathematical statistics; it should cover most of what you need to know, and it explains concepts to a great depth.
However, there are some additional topics that Wasserman's "All of Statistics" covers; I encourage you to compare their tables of contents to learn more. Pleasantly, it is also fairly clear - but only for students who are prepared to study at that level. If you have NOT learned mathematical statistics from introductory books, then "All of Statistics" will be difficult to digest.
Thus, if you have never learned mathematical statistics properly, then start with the 2 other books that I suggested earlier:
"Probability and Statistics for Engineering and the Sciences" by Jay Devore
"Introduction to Mathematical Statistics" by Robert Hogg, Joseph McKean, and Allen Craig