Nonparametric repeated significance tests for some analysis of covariance models

For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed. These procedures rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation. The basic theory is based on the weak convergence of certain stochastic processes relating to the rank order statistics. Various properties of the proposed tests are discussed.