We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the...

Suppose that one observes a process Y on the unit interval, where dY(t) = n 1/ 2f(t)dt + dW(t) with an unknown function parameter f, given scale parameter n N 1 ("sample size") and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such...