Testing Covariate and Interaction Effects in Fully Nonparametric ANCOVA Model

ABSTRACT
We consider the fully nonparametric ANCOVA model proposed by Akritas, Arnold and Du (2000) and propose methods to test for the covariate effects and interaction effects between the covariate and the treatment. This nonparametric model allows the covariate to influence the response in a possibly nonlinear and nonpolynomial fashion, the responses to be nonnormal or heteroscedastic, the covariate to have different stochastic distributions in different groups. The nonparametric hypotheses are invariant under the monotone transformation of the data. The test statistics have close relations with some recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. The test statistics are very easy to compute and have asymptotic normal laws under the null hypotheses. Simulation results and real data analysis will be presented. The methods we developed here have applications in some other interesting nonparametric testing problems, which will be briefly discussed.
 
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College of Natural Sciences