I am looking for a nonparametric statistical theory textbook that does not avoid tools from measure-theoretic probability and covers proofs on topics outside of rank-based hypothesis tests: e.g., kernel density estimation, nonparametric estimation, and resampling methods (i.e., bootstrapping, jackknife).

The closest textbook I can find to this is Tsybakov's Introduction to Nonparametric Estimation. What can I use to supplement this textbook?

Wasserman's All of Nonparametric Statistics has the appropriate topic coverage, but does not really cover proofs.

  • $\begingroup$ Do you think Tsybakov's book is good for beginners who want an introduction that isn't as proof or measure theory heavy? I searched for it and found some small previews which make it seem good, but I couldn't tell for sure. $\endgroup$ Aug 13, 2020 at 19:54
  • 1
    $\begingroup$ @roundsquare If you want to avoid proofs and measure theory entirely, something like Bishop's Pattern Recognition and Machine Learning would do. $\endgroup$ Aug 13, 2020 at 20:55
  • $\begingroup$ Thanks @Clarinetist. I took a look at the table of contents - it doesn't seem to be focused on nonparametric estimation - at least to me since I don't know much about the subject. Is that the focus of Bishop's book? $\endgroup$ Aug 14, 2020 at 20:54
  • 1
    $\begingroup$ @roundsquare It is not, but it covers the basics avoiding measure theory and proofs. In all honesty, I haven't seen a single nonparametric estimation that avoids proofs entirely. Another book to consider might be Semiparametric Regression by Ruppert, Wand, and Carroll - but be warned, this text is quite dense. I would honestly recommend you ask a question too; you'll probably get better recommendations that way. $\endgroup$ Aug 14, 2020 at 20:59
  • $\begingroup$ Thank you very much for asking this question! I only saw rank-based proofs before since the nonparametrics course clashed with other coursework I had to take. After finding Györfi et al's book, I also picked up a copy. $\endgroup$
    – kurtosis
    Aug 15, 2020 at 22:04

2 Answers 2


I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty of use of dominated convergence and Fatou's Lemma, and it hits topics like kernels and k-nearest neighbors.

The online notes from László Györfi seem like a smaller (i.e. much less complete) version of what you are looking for: there are sigma fields, dominated convergence proofs, etc. Maybe take a peek at that to see if you want to investigate the larger book by him and coauthors.


There's a chapter in this book on nonparametric statistics: "Modern Statistical Methods for Astronomy With R Applications", Feigelson and Babu https://www.cambridge.org/us/academic/subjects/physics/astronomy-general/modern-statistical-methods-astronomy-r-applications?format=HB&isbn=9780521767279


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.