Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

1Introduction

For every complex question, there is a simple answer and it is wrong.

H. L. Mencken

Jacob Wolfowitz first coined the term nonparametric, saying “We shall refer to this situation [where a distribution is completely determined by the knowledge of its finite parameter set] as the parametric case, and denote the opposite case, where the functional forms of the distributions are unknown, as the non‐parametric case” (Wolfowitz, 1942). From that point on, nonparametric statistics was defined by what it is not: traditional statistics based on known distributions with unknown parameters. Randles, Hettmansperger, and Casella (2004) extended this notion by stating that “nonparametric statistics can and should be broadly defined to include all methodology that does not use a model based on a single parametric family.”

Traditional statistical methods are based on parametric assumptions; that is, the data can be assumed to be generated by some well‐known family of distributions, such as normal, exponential, Poisson, and so on. Each of these distributions has one or more parameters (e.g. the normal distribution has and ), at least one of which is presumed unknown and must be inferred. ...