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

Joel L. Horowitz, Vladimir G. Spokoiny

Research output: Contribution to journalArticlepeer-review

208 Scopus citations

Abstract

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 nontrivial 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.

Original languageEnglish (US)
Pages (from-to)599-631
Number of pages33
JournalEconometrica
Volume69
Issue number3
DOIs
StatePublished - Jan 1 2001

Keywords

  • Asymptotic power
  • Hypothesis testing
  • Local alternative
  • Uniform consistency

ASJC Scopus subject areas

  • Economics and Econometrics

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