I'm a first-year graduate student working on probability and I am learning statistical inference by myself, I have skimmed through a few books like Casella /Hoggs but I find they omitted lots of details, for example, they didn't introduce the conditional expectation, so there are only proofs in discrete case about "sufficient statistics " "factoring theorem ", etc. could you recommend me a book for graduates or doctor degree that cover basic ideas of statistical inference and rigorous proofs? thanks!
Asked
Active
Viewed 1,906 times
6
-
3One book that I would not recommend is "Mathematical Statistics" by Shao. In my opinion this book takes formality too far and attempts to subsume everything within measure theory, which I don't think is a particularly useful approach. "The Theory of Point Estimation" and "Testing Statistical Hypotheses" by Lehmann seem to be quite popular. – dsaxton Mar 31 '16 at 13:23
-
1There are several good recommendations here: http://stats.stackexchange.com/questions/33197/advanced-statistics-books-recommendation For you, especially Young and Smith, Essentials of Statistical Inference. – kjetil b halvorsen Mar 31 '16 at 13:47
-
1Then how about first probability (Probability and Measure by Billingsley), then statistical inference (Trilogy by Lehman: Theory of Point Estimation, Testing Statistical Hypotheses, Elements of Large Sample Theory)? – Zhanxiong Dec 11 '17 at 04:53
3 Answers
2
One book not mentioned above which I quite like is Theoretical Statistics, Topics for a Core Course by Keener. It is relatively rigorous but quite readable at the same time. Personally though, I think a subset of Theory of Point Estimation by Lehmann, Mathematical Statistics by Shao, and Keener should cover almost all the topics at the level you want.
Gosset's Student
- 348
- 2
- 11
1
Take a look at Testing Statistical Hypotheses by Erich Lehmann and Joseph Romano. I also like Statistical Inference by Casella and Berger.
dimitriy
- 31,081
- 5
- 63
- 138
