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I'm looking for an book on statistics that's similar to Michael Spivak's Calculus. It should be rigorous, starting with some fundamental axioms and build layers of theorems on top of it, and it should be concise.

GNUSupporter 8964民主女神 地下教會
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user1299784
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  • https://math.stackexchange.com/questions/2281243/a-good-book-for-introduction-to-mathematical-statistics – GNUSupporter 8964民主女神 地下教會 Feb 04 '18 at 18:48
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    Calculus is structured that way, but statistics isn't. Good statistics books aren't either. – kimchi lover Feb 04 '18 at 19:02
  • Related: https://mathoverflow.net/questions/31655/statistics-for-mathematicians – symplectomorphic Feb 04 '18 at 19:26
  • The concisest might be Silvey's Statistical Inference; if you want a book that covers the prerequisite probability theory, you'll need something longer. There are plenty of books called "mathematical statistics" that do things axiomatically, in definition-theorem-proof style. – symplectomorphic Feb 04 '18 at 19:29
  • A rule for picking excellent applies does not necessary lead to picking excellent oranges. – BruceET Feb 04 '18 at 21:08
  • @BruceET: Well, for some people's taste, the best way to serve an orange is to replace it by an apple :) – PhoemueX Feb 04 '18 at 21:37
  • I'm not familiar with Spivak's Calculus book, but I have his Calculus on Manifolds book. If they are similar then this book is a good rigorous book of a similar style. It isn't so technically demanding that it's unapproachable, but is well written and concise while covering many topics. – Ryan Warnick Feb 05 '18 at 05:35

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I would suggest the book by Kiefer which is based on the course he taught at Cornell University. It requires very little prerequisites and builds up the modern theory of statistical inference. I personally think it is a great introductory book on statistical inference.

Hikaru
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