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I am about to complete my master's degree in Statistics at a very well-respected university and one which has a top 5 statistics department in the U.S. (all I have left to do is defend my thesis). I also have a BS Statistics from a top U.S. University as well. Even though I'd like to, I'm doubtful I'll go on to complete a PhD given that (a) I'm older and (b) I work full time.

That being said, I'm very much interested in continuing my studies of statistics in my own time. It seems like one thing I don't have much exposure to formally, but which every PhD statistics student seems to have a good understanding of, is measure theory. Given my background and my desire to learn this material, could the Cross Validated community recommend some introductory measure theory materials and some additional statistics books that you think might be a must-learn or a great way for me to essentially learn some "PhD-level" statistics on my own time? If it's helpful for the recommendations, my interests include survey sampling (especially small area estimation) and imputation, causal inference, longitudinal data analysis and analysis of correlated data.

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    $\begingroup$ My understanding was that Master's level and PhD level courses are the same -- it's just that the PhD student, after completing, during the first two years, the equivalent of a Master's degree, then goes on to work full-time doing research for the university, whereas the Master's student leaves, so the Master's student has to pay tuition for those courses while the PhD student does not. So seemingly you might already know "PhD-level" statistics. $\endgroup$ – Chill2Macht May 13 '17 at 8:23
  • $\begingroup$ Have you looked at stats.stackexchange.com/questions/231092 and stats.stackexchange.com/questions/70545? How about stats.stackexchange.com/questions/6538? $\endgroup$ – whuber May 13 '17 at 19:26
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My recomendation: Start here: Measure Theory Made Ridiculously Simple.

Then buy and read Burrill. I know its old, but its super inexpensive on Amazon and a really good read. It covers basics of Real Analysis and Probability Theory.

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