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What would be a good book for non-parametric statistics. Not just the introduction but advanced level. Also I am looking at something I can use for learn and not for reference.

In particular I am looking for a book that can contain basics behind non-parametric methods, non-parametric inference, methods to evaluate non parametrics, e.g., KS test, $t$ test, etc. , bootstrapping ....

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    $\begingroup$ Nonparametric statistics is a large field, but I'd guess All of Nonparametric Statistics by Larry Wassermann should be a reasonable starting point. I don't know if I would call it "advanced level" but he sketches the proofs of many of the results in the book. Topics include the bootstrap, smoothing techniques, density estimation, regression, and lots of other things. No nonparametric Bayes, however. $\endgroup$
    – guy
    Commented Mar 4, 2013 at 21:41
  • $\begingroup$ I have checked that one out but its more like a reference book than learning material. No? $\endgroup$
    – I J
    Commented Mar 4, 2013 at 22:42
  • $\begingroup$ I disagree, it should be fine for learning from. If I'm remembering correctly, he wrote it for people who hadn't seen nonparametric methods before, such computer science students he teaches. $\endgroup$
    – guy
    Commented Mar 4, 2013 at 23:18
  • $\begingroup$ Are you looking for 'distribution free' stuff, or nonparametrics in the sense of "infinite parametric", whether it applies to distributions, relationships between variables or whatever else? For example, I can assume a linear relationship for $(Y|X=x)$ without a distributional assumption, or I can assume that $Y$ is normal and not assume the relationship with $X$ is anything but 'smooth'... both can be referred to as 'nonparametric', even though each is parametric in one aspect (if potentially infinite-parametric in another). $\endgroup$
    – Glen_b
    Commented Mar 5, 2013 at 0:50
  • $\begingroup$ I am looking for distribution free stuff . $\endgroup$
    – I J
    Commented Mar 5, 2013 at 3:02

4 Answers 4

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I think of the Encyclopaedia Britannica of nonparametric statistics as being:

I'm not sure if I would characterize this as introductory or advanced. Many of the sections are a bit terse, in my opinion, and are written with a good deal of mathematical notation. This will be intimidating / off-putting for people who have some math anxiety. On the other hand, it's not really deriving theorems, it's just using mathematical notation to express the ideas. There are some problems included at the end of each section; you could definitely use the book to learn nonparametric statistics.

For a treatment that is much more introductory:

will be much less intimidating, I think. I have skimmed some portions of it, and it seems to be a gentle introduction for people who don't have a strong statistical background. It is very clear, but does not have anything like the depth or coverage of Hollander & Wolfe.

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  • $\begingroup$ I don't have a recommendation for a book that focuses primarily on the mathematical theory behind nonparametric statistics. $\endgroup$ Commented Apr 20, 2013 at 3:57
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    $\begingroup$ In november 2013 the third edition of Hollander & Wolfe appeared and a corresponding GNU R package NSM3 is available. $\endgroup$ Commented Jun 26, 2014 at 2:18
  • $\begingroup$ I find it confusing how you refer to the Encyclopaedia Britannica, when in fact the book does not come from the Encyclopaedia Britannica. In fact, the Encyclopaedia Britannica has an entry on nonparametric statistics. $\endgroup$
    – ahorn
    Commented May 16, 2020 at 6:40
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    $\begingroup$ I think @gung-ReinstateMonica was just writing figuratively and alluding to a source that is a reference, large and definitive. $\endgroup$
    – Nick Cox
    Commented May 16, 2020 at 8:00
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You may want to check out All of Nonparametric Statistics, by Larry Wasserman. The title says it all ;) The reviews for the book are outstanding. I cannot tell for myself, since I have not read it yet. But it seems to have all the theoretical background you are looking for, plus it has also a focus on applications, i.e. it well help you to put those techniques into use quickly.

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    $\begingroup$ Provide the name of book in the answer, not only the link, please! :) $\endgroup$
    – Ronie
    Commented Mar 13, 2018 at 1:38
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    $\begingroup$ Despite the title, this isn't a book that focuses on Wilcoxon-Mann-Whitney, Kruskal-Wallis and that bundle of nonparametric significance tests, which many readers of this thread may be looking for. As always, you can check out a book's aims and contents from material or Amazon or the publisher's website. $\endgroup$
    – Nick Cox
    Commented May 16, 2020 at 8:23
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Nonparametric statistics is to a good extent a disjoint collection of tests and estimators. Especially for tests, I suggest instead using semiparametric regression models as a unifying framework. Commonly used tests such as the Wilcoxon and Kruskal-Wallis tests may be obtained as special cases of the proportional odds semiparametric ordinal logistic regression model. A better rank-based approach than the Wilcoxon signed-rank statistic may be obtained likewise. The regression framework easily extends to allow covariate adjustment and longitudinal data.

I’ve taken this approach in my introductory e-book BBR.

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The best nonparametric statistics book is

  • Hollander, M.; Wolfe, D.A.; Chicken, E. Nonparametric statistical methods. Hoboken: Wiley, 2014. 848 p.

Lehmann’s book is a classic, but it doesn’t cover all the methods in Hollander et al. It has a balanced mix of teaching, practical examples, useful exact tables, and nifty proof sketches in the appendix.

  • Lehmann, E.L. Nonparametrics: statistical methods based on ranks. New York: Springer, 2006. 480 p.

The main focus of Hettmansperger’s book is rank-based methods, leaning towards a more rigorous style. The books by Randles & Wolfe and Gibbons & Chakraborti have a somewhat similar approach:

  • Gibbons, J.D.; Chakraborti, S. Nonparametric statistical inference. Boca Raton: CRC Press, 2021. 694 p.
  • Hettmansperger, T.P. Statistical inference based on ranks. New York: Wiley, 1984. 380 p.
  • Randles, R.H.; Wolfe, D.A. Introduction to the theory of nonparametric statistics. New York: Wiley, 1979. 450 p.

Conover and Siegel & Castellan wrote great books with a more practical, applied treatment. They also describe a few techniques that aren’t in the books I mentioned above.

  • Conover, W.J. Practical nonparametric statistics. New York: Wiley, 1999. 608 p.
  • Siegel, S.; Castellan Jr., N.J. Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill, 1988. 399 p.
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