I'm fairly mathematically inclined — had 6 semesters of Math in my undergrad — though I'm a bit out of practice and slow with say partial differential equations and path integrals my concepts come back with a bit of practice. I have not had a course on mathematical proofs (mathematical thinking) or one on analysis.
I also understand graduate level probability — have studied it formally and refreshed my knowledge lately.
I also have had a couple of graduate level courses on statistics and statistical learning.
I want to, out of personal interest, study mathematical statistics over the next 18-24 months. I'd like to devote an average of 5 hours a week of self study to the subject.
I am a bit at a loss on how to do it. I tried studying from the Casella and Berger book but really could not make any headway. I found the book a bit boring and its method intractable.
What I found difficult about Casella and Berger:
- Embarrassed to say this but the starting for the type setting — the way it was packed to reduce white space wore me down
- There are a lot of proofs that were there but I felt there was a lack of intuition on why we were trying to achieve the results and what was the larger goal at hand.
- The referencing of proofs from previous chapters was in a way that made the material a bit intractable to me — I was going back a lot until I finally gave up.
- The example seemed to be very doable however I could not tackle the problems — the problems seemed to be in a class by themselves.
- I just could not get into the material — and I wonder if the way my mind works I need a more rigorous treatment — should I consider a measure theoretic approach to mathematical statistics?
So question: is there a textbook that someone in my shoes could just study off of and teach themselves the subject.
What I would like in a text:
- In many ways the stuff I'd like in a book are the inverse of things I didn't like in Casella and Berger.
- The type setting of the book would help. Some of the points below will elaborate this point.
- I think it would be good to have a book which starts of with an intuition on what we would like to do, perhaps in a non-mathematical sense — somewhat like the book Statistics by Freeman et al.
- A book that presents the theorems in a simultaneous mathematical derivation and commentary format — In CB, I just gave up on trying to read up on the proofs
- A book that has a good range of solved problems accompanying each section.
- A book that also has computational exercises that allow the reader the build a better understanding by exploring the concepts say using R
- A book that covers the material that would be required for the first one or possibly two graduate courses in Mathematical Statistics.
- I am aware of this question Introduction to statistics for mathematicians — and there is some overlap and some of the answers I've studied before posting this question — however I feel that the two questions have different asks.