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I've been studying statistics for almost a year now, but I feel like I can't advance any further. I've tried by attending advanced classes, but even when I already know the topic I still don't understand a lot of things. For example, sometimes the professor shows a proof of some theorem and adds or deletes something and I really don't know why.

I've tried to study more high-level texts (such as Casella-Berger "Statistical Inference") but I wasn't able to understand most of the content. What I'm asking here is something (maybe an intermediate book or online course?) to go beyond my actual level before I dive into a more advanced book.

For example, as I said, I cannot understand Casella-Berger. Can you suggest me something like "OK, study this book and that book and after that you'll be able to understand Casella-Berger".

EDIT: I'll try to clarify my question as best as I can. I have a background in economics (but I think it can be generalized to any non mathematical-statistical-physical subject) and I want to apply for a PhD in statistics. My professor suggested to me the Casella-Berger book (saying: "but maybe it's too hard for you...". He was right, it was too hard). I've spent months studying and I feel like I gained nothing because I've understood something like 10% of the content.

The books I've studied so far are:

  • Statistics for Business and Economics by Newbold, Carlson, Thorne

  • An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani

  • a few specific topics from various sources

The reason I want to learn all of this is that I'm reading a lot of papers and they are very obscure to me. I can understand the introduction sometimes, but when it comes to the methods part there are statements, proofs, etc. and I feel completely lost after a couple of minutes. I can't see myself writing a paper in the future if I don't get more knowledge in statistics. Maybe I'm wrong but, in my idea, if I'll be able to tackle the CB book I'll be able to understand (almost) any paper.

Thanks Glen_b -Reinstate Monica and whuber for your suggestions, I've read the other topics and they've been useful. My request though is more about a path than a single book. Calculus is, for sure, something I should start studying.

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    $\begingroup$ There are many questions and answers on site with useful references that might help to bridge the gap. e.g. look at these: stats.stackexchange.com/questions/162393/… stats.stackexchange.com/questions/155018/… stats.stackexchange.com/questions/434961/… ... a few searches should turn up other possibilities $\endgroup$
    – Glen_b
    Commented Apr 28, 2020 at 13:16
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    $\begingroup$ This question is vague because it doesn't clearly describe the level at which you're at: it only says you are looking for material somewhere up to advanced undergraduate texts. Could you be more specific? For instance, it's possible you need to learn some Calculus first. Or maybe return to a modern introductory statistics methods text. Or study some scientific disciplines to learn how statistics is applied. It's impossible to tell, yet, from your description. $\endgroup$
    – whuber ♦
    Commented Apr 28, 2020 at 13:25
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    $\begingroup$ Unfortunately, reading C&B will not give you the ability to comprehend any paper. If that were the case, I'd be busy reading a lot of academic literature. It grants you the fundamentals, but you will likely need to sequentially read through papers until you can get an understanding of the "cutting edge" stuff! $\endgroup$
    – Ron Snow
    Commented May 2, 2020 at 16:22
  • $\begingroup$ Does this answer your question? Path to mathematical statistics without analysis background: ideal textbook for self study $\endgroup$
    – user304564
    Commented Aug 23, 2021 at 7:15

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Within the last three years, I have made my way from calculus to graduate-level math stats. I can speak to you from this experience.

First of all, I think it's great that you want to further pursue statistics. I made this decision when I took calculus 2- integration calculus. I highly recommend that you study what is usually regarding as Calculus I and II. I am sure that some people would recommend you go all the way to Calculus III. Personally, I have not used a lot of Calc III, yet.

Linear algebra is essential, and I would argue that you learn matrix theory beyond what is taught in an introductory linear algebra course. This content is obviously very essential in regression, but it comes up elsewhere in statistics, too.

Depending on how far you want to go into statistics, I would highly consider learning some real analysis. The more, the better. I think the equivalent of a one-year course in most undergraduate programs will be a sufficient start.

You've listed several textbooks that are introductory and that's great. While you're looking into these subjects I laid out for you above, you may start to realize that you've seen some of them in action in the material you've already been exposed to.

Notice that everything I have listed this far is not statistics. After you learn this material, you will be ready to read through some of the more advanced texts like Casella and Berger for math stats or graduate-level probability theory.

Regarding the different paths within statistics to focus on, I highly recommend mastering the basics of probability theory and math stats. From there, most branches of statistics will be available with some slight discomfort.

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    $\begingroup$ Thank you for your suggestions and advice Ron Snow. Do you know any good text for Calculus 1? I've borrowed Apostol - Calculus from my library but it seems a little ehm... "old style". $\endgroup$
    – Paolo
    Commented May 2, 2020 at 18:47
  • $\begingroup$ James Stewart's Essential Calculus: Early Transcendentals is what I used. It's amazing. It covers all of the material taught in standard calc I-III course across the US, and it covers it all very well. Also, since it's a pretty standard text, you can find solutions to most even problems online (odd problems are in the back). $\endgroup$
    – Ron Snow
    Commented May 2, 2020 at 18:53
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    $\begingroup$ Thanks Ron Snow, I'll start with that! $\endgroup$
    – Paolo
    Commented May 3, 2020 at 20:11

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