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I'm trying to pick a book to learn out of for the advanced undergrad/early grad level. I've heard of several popular books (in alphabetical order):

  • Casella, George and Roger Berger. Statistical Inference.
  • DeGroot, Morris and Mark Schervish. Probability and Statistics.
  • Rice, John. Mathematical Statistics and Data Analysis.
  • Wackerly, Dennis; William Mendenhall and Richard Shaeffer. Mathematical Statistics with Applications.
  • Wasserman, Larry. All of Statistics.

  • ...Others I may have missed...

What are the characteristics of these? I am especially interested in

  • Substantive focus
  • Prerequisite knowledge
  • Depth of coverage
  • Focus on intuitiveness or on mathematical rigor
  • Clarity of explication
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  • $\begingroup$ What are you trying to learn? Just advanced statistically theory or applied? $\endgroup$ – Lauren Goodwin Jul 21 '15 at 22:12
  • $\begingroup$ I'm looking for theory material. $\endgroup$ – Hatshepsut Jul 22 '15 at 3:46
  • $\begingroup$ Minor mistake but it is Mark Schervish, not Michael. $\endgroup$ – JohnK Jul 22 '15 at 8:20
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All Of Statistics is quite popular but I don't like it that much to be honest. It is mostly suited for a crash course and provides very little detail along the way. Its basic pro is that it covers a lot of diverse topics from Machine Learning to Poisson Processes but I don't think it makes your life easy with the exposition, most of the time you will have to research the topics further.

I don't think Casella and Berger is an undergrad book, it is more advanced than everything else and contains elements of measure theory. You might still be able to handle it if you are careful and patient but If you are an undergrad I suspect you will want to understand the ideas first. Of all these books that you mention my favourite in that regard is Probability and Statistics by Degroot and Schervish. You might also want to look into Introduction to the Theory of Statistics, a.k.a MGB. Both of these books go to great length in order to provide intuitive explanations for the important concepts, such as sufficiency, without disregarding mathematical rigor. For Probability and Statistics, there also exists a very detailed solution manual in the case you would like to try solving the exercises.

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