<p>An energetic community member has proposed a substantial tag wiki for the <a href="https://stats.stackexchange.com/questions/tagged/nonparametric" class="post-tag" title="show questions tagged &#39;nonparametric&#39;" rel="tag">nonparametric</a> 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.</p>

<p>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.)</p>

<blockquote>
  <p>'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.</p>
  
  <p>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 &amp; 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.</p>
  
  <p>'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.</p>
  
  <p>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.</p>
</blockquote>
