I am a beginning PhD student in biostatistics and want to learn about high-dimensional statistics. I have looked into the books by Buehlmann/Geer, Wainwright, and Giraud, but they seem to be targeted at researchers: for example, the derivations are sometimes hard to follow and there is little help on practical issues. Do you have any recommendations? Preferably something with R code?
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1$\begingroup$ It is more common to ask about multivariate statistics. MV-stats is going to be largely similar to 'high-dimensional', unless you are really just interested in problems like 'the curse of dimensionality' or $p>n$. Is that specifically what you're after? Can you clarify the problems / analyses you want to study? $\endgroup$– gung - Reinstate MonicaCommented Aug 13, 2022 at 20:37
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2$\begingroup$ Thanks gung. I know some multivariate statistics already; I am specifically interested in high-dimensional statistics. For example, I am interested in genomic problems, where we have many genes (~20k) but much fewer samples (~100-1000). $\endgroup$– RamonaCommented Aug 13, 2022 at 20:42
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The book "Fundamentals of High-Dimensional Statistics" by Lederer should be what you want: it is very well written, explains all details, and contains R labs. The first chapters explain the main ideas in a very accessible way. The later chapters are about the mathematical foundations of the topic; they are a bit harder but still worth the read.
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2$\begingroup$ Thanks for the suggestion! The book looks awesome, a lot of deep (also mathematical) insights but introduced in baby steps, so even I understand. :-) And the R labs look very practical too (did not look into them in detail yet). $\endgroup$– RamonaCommented Aug 14, 2022 at 4:50
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You mention interest in genomic problems, with 1000s of genes but 100s of samples. Brad Efron's "Large Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction" might be a good fit. The back of the book blurb starts out with:
We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem...
He uses an Empirical Bayes approach to show links between Frequentist and Bayesian perspectives on what to do when testing 1000s of hypotheses or making 1000s of estimates or predictions at once.
Efron has posted the table of contents and prologue here:
https://efron.ckirby.su.domains/other/2010LSIexcerpt.pdf
and provides R code and datasets here:
https://efron.ckirby.su.domains/LSI/datasets-and-programs/datasets.html
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2$\begingroup$ whilst I like his approach, the book is clearly not a textbook for that reason. $\endgroup$– seanv507Commented Aug 14, 2022 at 7:50