An adaptive, rate-optimal test of linearity for median regression models

J. L. Horowitz*, V. G. Spokoiny

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


This article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate. The test does not require knowledge of the distribution of the model's random noise component, and it permits conditional heteroscedasticity of unknown form. The numerical performance and usefulness of the test are illustrated by the results of Monte Carlo experiments and an empirical example.

Original languageEnglish (US)
Pages (from-to)822-835
Number of pages14
JournalJournal of the American Statistical Association
Issue number459
StatePublished - Sep 2002


  • Hypothesis testing
  • Local alternative
  • Uniform consistency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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