A good book on Statistical Inference?

probability-theory reference-request statistics book-recommendation

Many people still swear by the pair of classics by Lehman et al Theory of Point Estimation and Testing Statistical Hypotheses. If you want something a bit more modern, I like Theory of Statistics by Schervish. It covers both the classical and Bayesian theory, but does not slight either of them. There is also Mathematical Statistics by Shao, that is structured much more like the non measure theoretic textbooks, starting with a whirlwind review of probability theory, and seems to be used as a textbook fairly often judging from the semi-incoherent negative reviews on Amazon.

Probably better than my limited opinion, see the answers to a similar question on MathOverflow.


Bickel and Doksum, if you can find the 1977 edition is very good. It is a high-level treatment of statistics from a mathematical (tho not measure-theoretic) standpoint.

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