Covariate-Matched One-Sided Tests for the Difference between Functional Means

Abstract

When testing hypotheses about the effects of different treatments, variation among covariates can become confounded with that between treatments unless the treatments are applied using paired covariates. In the context of unpaired covariates, we propose implicit covariate-matching methods for testing the hypothesis that one treatment effect is greater than another. The methods are founded on the assumption that the mean treatment effect, conditional on the covariate, is a smooth function of the covariate. They are implemented using new interpolation techniques for nonparametric curve estimation. Bootstrap arguments are used to construct critical points. We show that even when the covariate distributions are identical for both treatments, covariate matching of the type that we propose produces tests of greater power than methods that do not attempt matching. Our techniques have application to two-sided hypothesis testing.