Nonparametrics: An overview

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  • Date: 28 Sep 2012

Strictly speaking, the term “nonparametric statistical techniques” implies an estimation or inference statement that is not directly concerned with parameters. These terms are therefore not exactly synonymous, yet the body of distribution-free techniques is perhaps more commonly known as nonparametric* statistical methods than as distribution-free methods.

Nonparametric methods provide valuable alternative techniques to classical parametric methods for many reasons. Nonparametric methods are sometimes called “weak assumption” statistics because the assumptions required for validity usually are quite general and minimal, at least much less stringent than those required for classical parametric methods. In many cases the procedures are inherently robust and even these weak assumptions can be relaxed. This property implies that conclusions reached by a nonparametric inference procedure generally need not be tempered by qualifying statements. Some other advantages are as follows: nonparametric methods (1) are easy to understand and apply, (2) are especially appropriate for small samples, (3) frequently require data measured only on an ordinal scale (inference procedures based on ranks), (4) may frequently be applied to “dirty data” (i.e., incomplete or imprecise data), and (5) have a very wide scope of applications. It is generally accepted that the history of nonparametric statistics dates back to Arbuthnott in 1710 (1) and his introduction of the sign test. However, most methods were not developed before the middle 1940s and early 1950s.

Taken from: Jean Dickinson Gibbons, Distribution-Free Methods, Encyclopedia of Statistical Sciences, 2006.

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