I am trying to read this book (Introduction to Mathematical Statistics by Robert,Joseph, Allen,7th edition) I find it hard to follow. So, can anyone please recommend another book has similar content? My background is Math bachelor level and I will continue my master in Stat next Fall. Thank you in advanced.
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do you know German language or would you be able to understand a german written book? – Seyhmus Güngören May 14 '17 at 23:55
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Is it hard to follow because of the mathematical level or the writing/presentation style? – V. Vancak May 15 '17 at 00:19
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No, I do not know German, but thanks anyway – May 15 '17 at 00:20
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I think it is hard because of the writing presentation. it is too many words hhh – May 15 '17 at 00:23
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https://math.stackexchange.com/q/1591466/321264 – StubbornAtom Apr 22 '20 at 20:06
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Does this answer your question? Are there any statistics texts which give both intuition AND justifications for the equations/methods? – Dec 29 '21 at 06:40
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My preferred textbook (note: it's quite expensive) is Mathematical Statistics with Applications by Wackerly et al..
Clarinetist
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Obviously I'm late to answer this, but I have some recommendations. As for a nice introduction, I can recommend Introduction to Probability and Mathematical Statistics by Bain and Engelhardt or Statistical Inference by Casella and Berger. On a slightly higher level is Mathematical Statistics by Shao. Finally, an older but still extremely useful text is Introduction to Mathematical Statistics by Hoel. One of the best treatments of (frequentist) statistics is the two-volume work consisting of Theory of Point Estimation and Testing Statistical Hypotheses, the former by Lehmann and Casella and the latter by Lehmann and Romano. PDFs of all can be found online if one looks in the right places.
If you're after a mathematical introduction to the ideas of probability underlying statistics, I can recommend two texts, Elementary Probability for Applications and a Probability: Theory and Examples, both by Durrett and both freely available. The first does not explicitly rely on measure theory while the second does.
These days, much interest is focused on Bayesian statistics, on which there are excellent (if not so numerous) mathematical treatments.
kandb
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How about Probability and Statistics Fourth Edition DeGroot/Schervish ? It's free online.
Vivek Kaushik
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I'll start with a general advice. To the best of my knowledge, a course in mathematical statistics usually has prerequisites like some introductory-level courses in probability and statistics (besides the basic standard mathematical courses like univariate and multivariate calculus). Sure, it is possible to grasp this material on-the-way, but I believe that it would be more effective to be familiar with some probability and statistics before delving into the mathematical aspects of statistical analyses.
Regarding the books themselves, personally, I liked Mathematical Statistics by K. Knight. IMHO, it has the "appropriate" mix of mathematical rigor and statistical intuition. But if you prepare very rigorous texts, then maybe you should try Asymptotic Statistics by A. Van der Vaart.
V. Vancak
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Mathematics for Machine Learning is another nice alternative (freely available) https://mml-book.github.io/
Lefty
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