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I will be starting graduate school in statistics in August. I purchased The Statistical Sleuth recently [you can view the table of contents by clicking on the "Look Inside" link], and I do think it is a great book.

However, I am the type of person who likes to learn theory alongside applications, i.e., in a theorem-proof-example setting, and this textbook seems to only emphasize practical examples over theory. I would just like to be given a formula and be provided a proof that it is true.

Does there exist a textbook that combines both of these theoretical and practical aspects?

Code examples wouldn't be necessary, but would be a huge bonus.

ETA: One textbook that I personally really liked was Mathematical Statistics with Applications by Wackerly et al., but that is at an undergraduate level and does not cover as many methods as The Statistical Sleuth.

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  • $\begingroup$ Feller's books have both theory and applications, they don't have the code examples. $\endgroup$
    – Aksakal
    Jun 1 '15 at 17:35
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    $\begingroup$ @Aksakal: Please clarify your suggestion. Which of Feller's books covers statistics theory broadly relevant to the table of contents at the link the OP provided? $\endgroup$
    – cardinal
    Jun 1 '15 at 18:03
  • $\begingroup$ Introduction to Probability Theory with Applications. $\endgroup$
    – Aksakal
    Jun 1 '15 at 18:05
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    $\begingroup$ @Aksakal: That is a probability theory text, not a statistics theory text. The set of overlap in topics with the book of the OP has measure (almost) zero. $\endgroup$
    – cardinal
    Jun 1 '15 at 18:12
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I think good bonafide data analysis examples will not often be found alongside proofs of statistical theorems in a single text. For graduate level studies, most Masters students do not touch proofs. They do work out sophisticated problems in probability, and so the programs tend to be "quantitative" but not really "mathematical". For PhD level students, graduate mathematical training is usually incorporated and proofs need to be grasped at the Lehman Casella level: measure theory and functional analysis primarily. If a book like that were to include data analysis examples, it'd be 2000 pages long!

The content in the book you link, however, is only good enough for an undergraduate degree with no calculus training. If you would like to be exposed to applied material appropriate for a graduate level statistician--and this means that integration, differentiation are regular parts of the development and discussion of concepts--there are many references out there.

Some of my favorite graduate level applied self-learning texts are:

  • Categorical Data Analysis - Alan Agresti
  • Probability Models - Sheldon Ross
  • Regression Modeling Strategies - Frank Harrell
  • Logistic Regression: A Self Learning Text - Kleinbaum and Kleine
  • Survival Analysis - Kleinbaum and Kleine
  • Longitudinal Data Analysis - Diggle Heagerty Liang Zeger
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