Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 822-835 |
| Number of pages | 14 |
| Journal | Journal of the American Statistical Association |
| Volume | 97 |
| Issue number | 459 |
| DOIs | |
| State | Published - Sep 2002 |
Funding
Joel L. Horwotz isiaChEaa.rnEldeamHsMmr. rnoiPrsoo,fessor Deparnt tof Ecomnomics,eNorthwserteUnnive, Evrastonsn,iILt602y08-2600 (E-mil: [email protected])Vlad.teimir G. Spokoiny is Prof-es sor, WeieInrstituste antdrHumbaolsdt sUnive, Mrohrensstirtsay39es, Berinl 10117 Grme(E-mail:[email protected])iWe.e thank RusllsDveid-a son and Jianqing Fan for helpful comments. The reasrof Jceoel hL. Horowtz i was supported in part by NSF grant SES-9910925 and the Axandlerevno Humboldt Foundation.
Keywords
- Hypothesis testing
- Local alternative
- Uniform consistency
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty