app_stat

+1 to the Casella and Berger recommendation. We used that as our primary book for our year-long Probability and Mathematical Statistics sequence, and I still refer to it regularly. However, if you plan to take a more theoretical approach in your program, you might want to consider Rick Durrett's books on probability and stochastic processes. The former begins with a chapter on measure theory, which should give you a sense of his approach to the rest of the topics. (Note that measure theory is not really addressed in Casella and Berger's treatment of probability.) Two great books for self-study: Linear Models in Statistics (Rencher & Schaalje): This book takes you through all the standard linear models (and then some) from a linear algebraic perspective (standard at the graduate level). Clear exposition and the inclusion of nearly all solutions distinguish this book from others on the same subject. If you have any interest in econometrics, this will be a good primer that should allow you to dive right into Hayashi's and Wooldridge's respective textbooks. A Course in Large Sample Theory (Ferguson): This was recommended by a professor as a complementary text to Casella and Berger. There's a more thorough treatment of asymptotics and convergence concepts here, plus this book also includes solutions in the back. Congrats on your acceptance!