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this is a subject that time and again shows up, and I've read old postings. Still: I am taking an intro class in statistics from a Math department (Junior/Senior level). It is pretty intense (it's statistics and probability) and has a strong math component (calculus as well as linear algebra are required and used throughout the class). Exercises are done using R most of the time. The book we follow is an unedited book from the lecturer, and it's OK, but even though it's strong in the math part, it doesn't give a lot of examples nor tackles the very important aspects of why we do some things or what's the importance of this or that. I read here that a lot of people love Sheldon Ross' books, but when I looked at them, the equation parts are way below what we are doing. Is there a book like that, but more in depth in the math part? Thank you so much for any suggestion and why.

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  • $\begingroup$ Statistical Inference by Casella & Berger is a good source. It is calculus based and does not involve measure theory, so it is appropriate for upper level undergraduate level. There is a pdf of the textbook and solutions manual freely available online. $\endgroup$ – user133631 Oct 14 '14 at 20:36
  • $\begingroup$ I looked at it. Very similar format/contents to my lecturer. Is there something less... dry? $\endgroup$ – user177142 Oct 14 '14 at 21:55
  • $\begingroup$ You basically want an applied statistics text that covers the major inferential procedures discussed in a mathematical statistics text at the undergraduate level. I don't know of any specific references, but consider that you may actually end up needing multiple texts to address this need, since applied texts tend to be focused on certain aspects of statistical practice (e.g., regression vs. ANOVA vs. estimation vs. Bayesian theory vs. hypothesis testing). $\endgroup$ – heropup Oct 15 '14 at 2:04
  • $\begingroup$ The book I referenced below covers both applied methods (ANOVA, Regression, Nonparametrics) but also includes advanced, but non-measure theoretic, discussion of theoretical issues like consistency, sufficiency, the most powerful tests (including Neyman-Pearson lemma), Cramer-Rao lower bounds and their use in MVUE, and bayesian vs frequentist methodologies. All of this is at at the upper undergrauduate level, so all you need is calculus and some basic matrix theory. Also, there are lots of questions...with answers to test yourself. $\endgroup$ – user76844 Oct 15 '14 at 14:40
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    $\begingroup$ Does this answer your question? Recommend a statistics fundamentals book $\endgroup$ – Intellectually disabled Dec 23 '20 at 3:03
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Consider Modern Mathematical Statistics with Applications by Devore and Berk. Its calculus based and uses a bit of linear algebra, but livens it up by applying it to real data and usually discusses motivations for methods. As a bonus, there are answers to a lot of the problems in the back of the book.

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