Nonparametric Tests of Inequality Restrictions
All of the above models and hypotheses were concerned with comparing means and/or variance parameters of either known or asymptotically normal distributions. We may not know the distributions and/or be interested in comparing more general characteristics than the first few moments, and the distributions being compared may not be from the same family. All of these situations require a nonparametric development that can also deal with ordered hypotheses.
Order relations between distributions present one of the most important and exciting areas of development in economics and finance. These include stochastic dominance relations which in turn include Lorenz dominance, and such others as likelihood and uniform orders. Below we focus on the example of stochastic dominance (SD) of various orders. An account of the definitions and tests is first given, followed by some applications.