An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative

We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothn ess of the alternative model and is uniformly consistent against alternativ es whose distance from the parametric model converges to zero at the fastes t possible rate. This rate is slower than n(-1/2). Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n(-1/2). There are, howeve r, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for whi ch the finite-sample power of our test greatly exceeds that of existing tes ts. This conclusion is illustrated by the results of some Monte Carlo exper iments.