Nonparametric Statistics: Rank-Based Methods

Abstract

From its early beginnings in the early 1900s, nonparametric statistics has been an active area that has stimulated elegant statistical theory and beautiful applications. Its development continues at a vigorous pace today. There are many reasons for the success of the nonparametric approach. Nonparametric methods have wide applicability and typically require only modest assumptions concerning the underlying populations from which the data are drawn. Under these mild assumptions, exact hypothesis tests, exact confidence intervals, exact multiple comparison procedures, and exact confidence bands can be obtained. Nonparametric methods have excellent efficiency properties with respect to their parametric competitors and are also robust in the sense that they are relatively insensitive to outlying observations and departures from the model. This article highlights some classical rank-based nonparametric methods in two- and k-sample location problems. These problems and their generalizations were central to the early development of nonparametric methods and remain extremely useful for data analysis today.