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I am going to start my PhD in Statistics next fall and I am currently studying some math (in part because I don't want to stay too much time without studying something and in part to be sure that I won't struggle with my courses in the first semesters).

I covered almost all Stephen Abbott "Understanding Analysis" and then I moved forward to "Principles of Mathematical Analysis" by Walter Rudin and "measures integrals and martingales" by ‎Schilling.

The fact is that besides Abbott's book the others are pretty big books, with hundred of pages and covering a wide sprectrum of topics and I am not really sure which chapters in particular I should study.

For those who have some experience with these (or similar) books, could you give me some brief idea on which topic I should put more attention?

Thanks in advance.

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closed as primarily opinion-based by whuber Aug 22 at 15:38

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ 0. Congrats on your dedication. 1. What are of Statistics you like? (Generally) 2. Depending on where you aim to study, a PhD supervisor at this point is a very crucial or very immaterial choice. eg. In UK PhD students work directly with a supervisor. If person X has no relation to the research interests of supervisor Y then X's chances are hindered when it comes to getting a PhD in collaboration with Y. Greece is effectively the same. In USA, you effectively have at least a year if not two to declare/find a supervisor as you are taking graduate classes. 3. How is our Lin. Algebra? $\endgroup$ – usεr11852 Aug 22 at 15:42
  • $\begingroup$ thanks for your rapid response, I am particularly interested in Time Series analysis, filtering and non linear regression. I am going to study in Italy, and as in USA , during the first year and a half (more or less) I will be following graduate courses- That being said, the fact is that I am an economist and I am somehow worried that my "quantitative" knowledge might be lower that the standard. $\endgroup$ – RScrlli Aug 22 at 15:48
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    $\begingroup$ Hmm.. I can see how this will lead to a discussion. Maybe you try to present this in the Ten Fold chat? $\endgroup$ – usεr11852 Aug 22 at 15:51
  • $\begingroup$ Since you seem to have a strong math background, I recommend you to study basic CS theories (Algorithm and database). Also, if you are interested in ML, element of statistical learning is a good starting point. $\endgroup$ – JaeHyeok Shin Aug 22 at 15:57
  • $\begingroup$ Congrats on your choice to go into a Stats PhD! The above advice is pretty great. I would only add to that I would also try to identify areas you feel weak and work on those. Intro statistics courses will be math heavy, so if you feel your calculus/analysis needs brushing up - then revisiting that would be worth it. $\endgroup$ – Samir Rachid Zaim Aug 22 at 18:30