I want to start learning statistics. I have taken proof-based Calculus 1 and 2, as well as two proof-based courses in Linear Algebra (1 and 2). What is a good introductory-level (but rigorous enough) book to start self-learning statistics? Also, if you know about any other resources (other than books) to help my self study, you can recommend them. Thanks in advance!
2$\begingroup$ Without an iota of doubt, go for Casella, Berger. Its prerequisites are modest and yet it provides a solid knowledge at a semi-rigor manner. Next would be Rohatgi. Another great book would be Almudevar. $\endgroup$– User1865345Jan 28 at 9:24
$\begingroup$ @User1865345 Thanks! Is Almudevar on the same level as Casella and Berger? Or is it more advanced? $\endgroup$– user926356Jan 28 at 23:34
1$\begingroup$ It's a bit advanced than C&B. But definitely comprehensive and slow paced for a new learner. On another note, you can look Keith Knight's book which has more coverage than C&B. Finally a light read would be Pestman. Point of recommending so many options is to let you have 2-3 books at once for you to study so that one may be taken as the main one and others as reference. $\endgroup$– User1865345Jan 28 at 23:42
Statistical Inference by Casella and Berger is the standard textbook for this. If you’re good at some elementary real analysis (say calculus at the level of Spivak, not necessarily Rudin), you have the mathematical background to handle most of it. Some multivariable calculus might be helpful to know, but the basics of partial derivatives and multiple integrals should be well within reach if you need to self-study them to understand some sections of Casella/Berger.