An energetic community member has proposed a substantial tag wiki for the tag. Because it includes so much, I thought it would benefit from the community participating in improving it here, rather than attempting to do so through the (extremely limited) wiki editing interface. Then, once the language stabilizes, we can modify the wiki itself. I am reluctant to approve it outright because, IMHO, not all the characterizations are as clear or correct as they ought to be for something intended as a general reference. But it's such a good start and such a devoted effort that I think it deserves our attention.

Suggestions can be made in the usual ways: replies, comments, and direct editing of this question itself. (Direct editing might be cleanest, but I'm not sure everyone will be able to carry that out.)

'Nonparametric' is a fairly broad term for a wide range of statistical analysis procedures that will still yield accurate results when classical assumptions are violated. As the term implies, the original idea was to develop techniques that did not attempt to estimate properties of the parameters (e.g., confidence intervals of the means) of the populations from which the data were sampled. Instead, these techniques were often based on ranks of the data and thereby afforded the calculation of correct p-values. A prototypical example would be determining the central tendency of a highly skewed distribution--the assumption of normality is violated, but methods based on the median would be unaffected.

Today the term is sometimes used to cover approaches (e.g., bootstrapping) that work in very different ways and are often used to work with estimated population parameters. As such, the concept is somewhat fuzzy. Nonparametric techniques can be compared and contrasted with several other types of statistical procedures, including semi-parametric & generalized additive models (which combine elements of both parametric and nonparametric approaches) and robust statistics that use alternative loss functions to minimize the influence of outliers and excessive skewness.

'Assumption-free' and 'distribution-free' are sometimes used as synonyms. Note that these terms, taken literally, are inaccurate descriptors of nonparametric procedures: Nonparametric analyses do entail assumptions, just fewer and ones that are more likely to hold. Moreover, nonparametric techniques typically rely on the uniform distribution (e.g., for rank-based procedures) or on estimated distributions (e.g., for bootstrapping), just not the normal distribution.

Lastly, although nonparametric usually connotes alternative statistical tests, it can be used to indicate an alternative approach to modeling. For instance, the simplest model of a dataset (assuming normality) is simply to estimate the mean and standard deviation, but a model of the data could be generated by kernel density estimation without ever calculating a mean.

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  • $\begingroup$ You seem to think it's not quite right, but don't want to turn it down either. I think that if I were a moderator, I would have a fairly light hand as well. You could approve it & then edit it to fix any problems (& likewise for similar situations in the future). It seems to me tag wikis should be reasonably editable. For a regular answer, egos would often be bruised if we went into someone else's answer and made major revisions (even though we have the privilege to do so), but no one owns the tag wikis--so, no feelings should be hurt. $\endgroup$ – gung - Reinstate Monica Mar 4 '12 at 8:32
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    $\begingroup$ @gung Tag wikis have strong restrictions with respect to editing (need to be in the 'top users' ) and reviewing (need to have a certain amount of rep). I think the basic idea here is to offer the community a way to discuss and improve this particular tag, that reflects a proeminent field in statistics, instead of leaving the last word to us, mods. $\endgroup$ – chl Mar 4 '12 at 21:47
  • $\begingroup$ @chl, that's fair, but I wonder if the ultimate answer is that it would be better if tag wikis were more readily editable. Tags can be created w/ 300 rep, questions re-tagged w/ 500 rep, questions edited w/ 2k rep; requiring 5k rep to edit a tag wiki may be too high. I count 17 CVers currently who meet that requirement, & many empty tag wikis. Perhaps 2k is enough to edit tag wikis, but 5k is required to accept edits from users w/ less, or some other scheme. BTW, I acknowledge these comments are not quite on topic; I have no problem w/ the community improving this tag here. $\endgroup$ – gung - Reinstate Monica Mar 4 '12 at 22:38
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    $\begingroup$ Gung, unlike most other moderation tasks, approving a tag wiki edit (or improving on one) can require good subject-matter knowledge and much thought and care. You are correct that a mod could "approve it & then edit to fix any problems," but that is a relatively heavy burden; often it's not a matter of just a few minutes' work. The hard part comes when it's clear that somebody without the reputation to suggest they are an expert has put a lot of effort into a tag wiki but their proposed text is not entirely correct or suitable--or maybe the mod just isn't sure. The community can help here. $\endgroup$ – whuber Mar 4 '12 at 23:42

I think it would be worth making it bullet pointed, and so somewhat more structured:

  1. Nonparametric exact test procedures based on ranks (the 1950s, reaching their apex with Mann-Whitney tests, and further in robustness theory with L-statisitcs; also, Kolmogorov-Smirnov test)
  2. Nonparametric inference procedures based on resampling (permutation tests)
  3. Nonparametric estimation procedures based on local approximations (kernel density, kernel regression, lowess)
  4. Other procedures that work without making strong assumptions about distribution of the data (design-based inference in survey statistics is sometimes referred to as non-parametric inference)
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