ABSTRACT
Non-parametric theory is concerned with problems involving larger families of possible distributions, families which cannot be labelled by a finite-dimensional vector-valued parameter. Often there are two possible approaches to a given problem in inference, the parametric and non-parametric. The former involves stronger assumptions than the latter about the family of possible distributions on the sample space, assumptions which may not be verifiable, and to this extent the non-parametric approach is more realistic. And again a parametric model may be used as a guide, both to suggest the statistics to be used and to yield a large-sample approximation to its permutation distribution. Methods were suggested for particular problems and only relatively recently have optimum properties of these methods been investigated.
