WIAS Preprint No. 617, (2000)

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


  • Horowitz, Joel L.
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G10 62G20


  • Hypothesis testing, local alternative, uniform consistency




This paper 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 accommodates conditional heteroskedasticity of unknown form. The numerical performance and usefulness of the test are illustrated by the results of Monte Carlo experiments and an empirical example.

Appeared in

  • Econometrica, 69, no. 3 (2201) pp. 599 - 631 under the title: An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative.

Download Documents