statistics for data analysis

Question

I am a last year math student, but I also want to learn a bit of data analysis in its theoretical aspect, many have told me that certain bases in statistics are needed, but I have only seen the course of probability and measurement theory Then I would like you to recommend a statistics book for data analysis

I want to clarify that I do not have solid knowledge in statistics, I only have knowledge in probability

Answer 1

It appears you have some background in probability in the context of measure theory; given that, I would suggest you look at one of:

• Shao, Mathematical Statistics
• Keener, Theoretical Statistics
• Schervish, Theory of Statistics

For a non-measure theoretic treatment:

• Bickel and Doksum, Mathematical Statistics (in two volumes)
• Casella and Berger, Statistical Inference

You will not only need a course in mathematical statistics, but one in linear models. Given your mathematical background, I would suggest either one of:

• Agresti, Foundations of Linear and Generalized Linear Models
• Monahan, A Primer on Linear Models
• McCullogh, Searle, and Neuhaus, Generalized, Linear, and Mixed Models
• Christiansen, Plane Answers to Complex Questions

Mathematical statistics and linear models are the core of almost everything in statistics. Once you've learned the contents of these two subjects, you could consider looking at Advanced Data Analysis from an Elementary Point of View by Shalizi, available at https://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/.