ok, i will try.
2 books I absolutely love and have read cover to cover several times, solved most of the 1000+ problems.
1. Inference - Rohatgi
2. Inference - Stapleton
Why I recommend them ? The real answer is super long. But the short version is - there are thinkers & there are doers. Basically, the mathematical statistics world has these theory-building Bourbaki type guys who write a LOT, say a LOT, but never get to the fucking point (imho). The opposite view is "math is bunch of tricks. its like chess - more middlegames & endgames you know, higher chance of winning. No real point in learning who originally came up with this particular middle game variation, or why does this opening work etc etc. Just learn the trick & play the game." So that's the eastern (Indian/Chinese) school of thought, which is what I subscribe to.
The 2 inference books listed above are essentially grab-bags of tricks. Do this - it works - now try it on these problems - ok next trick...on & on. So I solved the 1000+ problems & now I know lots of these methods that just work.
eg. recently i was asked - some vc's are evaluating a startup. their valuations are $1 million, $4 M,$10M, $20M, $50M. what's your evaluation & why ?
so i'm thinking - hey isn't this just rohatgi taxicar ? so i quickly said- sum is 85, times 1/5 is 17. Whereas largest observed is 50, times 6/5 is 60, so half is 30. since 50 was max observed, another estimator is half that, ie. 25. if you want doctor's estimate, get rid of 1 and 50, then sum is 34 so times 1/3 is 11.3
so then we have 4 estimators, - the sample mean is 17 million, its the method of moments estimator, clearly unbiased but high mean square error because variance is high. the maximum likelihood estimator is 25 mil, and has smallest variance, but the mse will not be the lowest since it is not unbiased so bias square will add. the 30 mil estimate is also unbiased, but has low variance so it has the lowest mse of the lot. the doctor estimator 11 million is unbiased but high variance and mse is in between. now if you want the absolute lowest mse, i can cook up a 5th estimator which has nonzero bias but mse will be the minimum....
at this point the interviewer interrupts me - you've never seen this problem because we came up with it in our last meeting at our firm. Yet you gave me 4 very good estimators under 2 minutes & want to cook up a 5th one that's even better. And you don't even have a phd. meanwhile i just spoke to an actual phd and asked him this same question, he went on and on for 20 minutes without giving me a single concrete estimator!
so that's the thing. rohatgi, stapleton, these are about real world, down & dirty, how to do stuff. how to solve actual problems.
whereas the gelman bda, the shao, the schervish, the lehman, the bickel & doksum - these were my prescribed textbooks. imho they are absolute garbage, worse than dirt. after the exam i threw them away. such bullcrap. they go on & on without getting anywhere & have practically zero good worked examples.
so that's my 2 cents. i still have the rohatgi & stapleton on my desk. sometimes i tear up when i look at them. they have taught me so, so much!