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One may find this question a duplicate, but my search through CrossValidated did not give satisfactory result. So I am posting this question and explaining what I want.

I need a book such that if one studies it - one knows he has no "white spots" in basic stats. On modern probability, in my opinion, the book of Olav Kallenberg (2nd edition) is such a book. It is also well composed and written. There are few other books getting close to it, but (in my opinion) they are worse.

There is huge number of books on stats and whenever I need to look up for something or recall something I never know which one to chose. So I just need one book in which I can look up for answers to basic (and "advanced") questions on any standard topic.

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    $\begingroup$ The Encyclopedia of Statistical Sciences? $\endgroup$
    – user603
    Mar 14, 2015 at 15:41
  • $\begingroup$ I guess I'm looking for a book that is suitable for both study and reference, so that if one needs to review/learn some topic - one could do it in one place on a good level and it fit into his knowledge of stats without requiring "digesting" another book or two. So it should be kind of encyclopedic, but encyclopedias don't qualify. $\endgroup$
    – user35953
    Mar 14, 2015 at 16:02
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    $\begingroup$ Did you find anything? I would be interested (I know Kallenberg's book well), but not sure such a book exists. I have previously used Casella and Berger Statistical Inference, which was OK. I recently came across "All of Statistics: A Concise Course in Statistical Inference" by Larry Wasserman, but not looked at it properly yet-- have you seen it? $\endgroup$ Mar 30, 2015 at 11:40
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    $\begingroup$ Schervish: springer.com/us/book/9780387945460 $\endgroup$
    – Zen
    Jul 19, 2016 at 21:35
  • $\begingroup$ Kendall & Stuart: Advanced Course in Statistics ? $\endgroup$ Apr 30, 2017 at 11:43

2 Answers 2

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Presumably the person who asked this question is long gone, but for future reference I will mention a book here. Note: I have not read this book.

Theoretical Statistics: Topics for a Core Course, by Robert W. Keener. Amazon: link.

I quote the last three lines of the review by Amazon user Der Boandlkramer:

This book is in a class by itself!

Its natural companion (and prerequisite, to some extent) textbook on probability is the monumental "Foundations of Modern Probability," by Olav Kallenberg.

For whatever it's worth, Keener's book is used at UCLA (STAT 200B).

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Peter Bickel and Kjell Doksum wrote Mathematical Statistics Volume 1 and Volume 2. The two books form a comprehensive guide to modern (frequentist) statistical methods at a level of mathematical sophistication similar to Kallenberg.

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