Abstract
This paper discusses the problem of testing the equality of two nonparametric regression curves against one-sided alternatives in a two sample heteroscedastic setting in which design and error densities may differ between the two populations. The paper proposes a class of tests using covariate matching and derives their asymptotic power for local alternatives. Using a semiparametric approach, an upper bound on the asymptotic power of all tests against a given local alternative is obtained. For a given local alternative, a member of the proposed class of tests is shown to achieve this upper bound.
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