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I would like to know a good book in statistics, that would interest me. I have before this spent a lot of time spent studying discrete mathematics and abstract algebra and i love its beauty and elegance. However i am yet to find something of the sort in statistics. Could you give me a few pointers?

I had taken an introductory course in probability and statistics(point, interval estimation, confidence intervals and all) and aced the exams but i find it to be pretty boring, mainly formulas. The problems(numericals) in statistics are pretty easy (relative to pure math), at least given in standard books. I have a lot of experience with theoretical mathematics and find it to be very beautiful are there something like this in Statistics?

I have already taken a glance across Casella and Berger, but the same thing it isnt intellectually challenging, like real analysis or modern algebra or topology

I would like to mention i am a dual CS and Math undergrad and i have a huge interest in theoretical Computer Science in general and algorithms in particular, so that you have an idea of my interests


marked as duplicate by kjetil b halvorsen, Peter Flom Mar 30 at 18:27

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    $\begingroup$ It depends on what you find interesting or challenging -- the information isn't much of an indication; it's hard to guess at your preferences for the different areas of statistics, theory vs practice and the various ways of presenting them. You may be better with some of the older works on probability first (Do you like Feller's volumes for example? An Introduction to Probability Theory and its Applications, Vol I and II. If so, you might find something like Kendall's Advanced Theory of Statistics somewhat interesting -- or you might find it boring. How could we guess?). $\endgroup$ – Glen_b Jun 19 '15 at 7:25
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    $\begingroup$ You might start by looking at some of the other questions asking for book recommendations or references and see if some of those questions seem relevant; if none do it will help you narrow your question a little further. $\endgroup$ – Glen_b Jun 19 '15 at 8:20
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    $\begingroup$ Re: Glen_b's first comment: See my answer in stats.stackexchange.com/questions/33776/… regarding Feller Vol. II. If you like abstract algebra, e.g., semi-groups, this could be a very good book for you. It's a probability, not a statistics, book, but what you learn and insights from the book should be very helpful in statistics. Maybe also find some material on the web on theoretical statistics, such as exponential families, but i don't have a specific reference to recommend in that area, but there is lots of stuff on the web. $\endgroup$ – Mark L. Stone Jun 19 '15 at 14:11
  • $\begingroup$ Because this question is not actually about statistics, but about statistics-as-mathematics, perhaps it belongs on Mathematics. $\endgroup$ – whuber Jun 19 '15 at 14:15
  • $\begingroup$ To learn statistics you really need to dive into some work with data! Many ways to do that. For some use of abstract algebra in statistics have a look at Persi Diaconis Group Representations in Probability and Statistics $\endgroup$ – kjetil b halvorsen Aug 14 '17 at 21:07