ABSTRACT
All of the specification tests emphasized in this paper can be put into a common nonparametric framework, and demonstrating and clarifying this framework in a variety of different situations is the main purpose of the paper. The key idea of our procedure is to construct two statistics, which estimate the same quantity under H0-for example linearity or independence-but different quantities under the alternative hypothesis HA-Moreover, a distance function is introduced measuring the distance between the statistics. The null hypothesis is rejected if a large value of the distance functional occurs. The critical value is derived from the distribution of the distance functional under H 0 . This distribution can either be constructed from asymptotic theory, often using a U-statistic argument, or from a randomization device. For small and moderate sample sizes it is our experience that the randomization argument gives a much better approximation than the asymptotics.
