Most mathematics (specially in statistics) books just mention the formula, and they don't mention the derivation of the formulas. Is there any book which has the derivation of the formulas?
closed as too broad by Lord Shark the Unknown, Brahadeesh, mrtaurho, Chris Godsil, ancientmathematician Mar 2 at 13:55
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I recommend Mathematical Statistics, A Unified Introduction written by George R. Terrell. As the title suggest, the author never separates statistics from abstract models in probability theory.
- Statistics proceeds and motivates concepts in probability theory.
- Many large-sample results accessible to undergraduates.
- Since math and statistics are treated in a unified manner, all results are proven.
However, after reading this introductory book, if you want to learn more advanced statistics, you'll probably need to learn measure theory. I recommend A User's Guide to Measure Theoretic Probability by David Pollard since it's also a book in which motivation precedes abstraction.
What you want is a book on the subject of mathematical statistics, of which there are many. The book that was used in the course I took was "Introduction to Mathematical Statistics" by Hogg and Craig. I think it's a good book, but I don't have enough experience with other texts to make comparisons. Some math stat books use measure theory, others do not. Hogg and Craig do not, which is probably right for a beginner.