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I would like to learn statistics rigorously. The only book that I can find that seems to do statistics rigorously is this book "Theory of statistics" by Schervish (which seems advanced):

http://www.amazon.com/Theory-Statistics-Springer-Series/dp/0387945466

Question 1: Are there other books that do statistics rigorously (and theoretically do not assume prior knowledge of statistics) ?

I took only an introductory non-rigorous course called "Probability and Statistics" that is taught for engineers at my university. I know analysis. I know some measure theory. I plan to finish the book measure theory by Halmos which has a chapter on probability theory (I'm currently self-studying it).

Question 2: If I finish the book measure theory by Halmos, will my background in probability theory be sufficient to learn the book "Theory of Statistics" by Schervish ?

Thank you a lot.

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If you know analysis including measure theory, you should be able to read Schervish. I don't recall that there's that much measure theory in it. You do need to know how to write mathematical arguments.

PS: I'm realizing deGroot & Schervish is what I had in mind when I wrote the answer above. Maybe I'll add more later. See comments below.

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  • $\begingroup$ Thank you a lot. You seem to be an expert in statistics so I trust your answer a lot. By the way, do you have any other suggestions for books that do statistics rigorously ? $\endgroup$ – Amr Jul 8 '15 at 14:05
  • $\begingroup$ Perhaps Lehman's Theory of Point Estimation and Theory of Hypothesis Testing. Serfling's Approximation Theorems of Mathematical Statistics is rigorous but it doesn't do the usual theory-of-statistics topics found in something like deGroot & Schervish. And now suddenly I'm realizing deGroot & Schervish is what I had in mind when I wrote the answer above. Probably something can be said for Bickel & Doksum, although I seem to recall being annoyed by the fact that they didn't assume the reader knows matrix algebra. $\endgroup$ – Michael Hardy Jul 8 '15 at 20:04

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