WIAS Preprint No. 542, (1999)

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


  • Horowitz, Joel L.
  • Spokoiny, Vladimir G.

2010 Mathematics Subject Classification

  • 62G10 62G20


  • Hypothesis testing, local alternative, uniform consistency, asymptotic power




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 fastest possible rate. This rate is slower than n-1/2. Some existing tests have non-trivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n-1/2 . There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.

Appeared in

  • Econometrica, 69, No. 3, (2001), pp. 599-631

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