Abstract
A new quantile regression concept, based on a directional version of Koenker and Bassett's traditional single-output one, has been introduced in [Ann. Statist. (2010) 38 635-669] for multiple-output location/linear regression problems. The polyhedral contours provided by the empirical counterpart of that concept, however, cannot adapt to unknown nonlinear and/or heteroskedastic dependencies. This paper therefore introduces local constant and local linear (actually, bilinear) versions of those contours, which both allow to asymptotically recover the conditional halfspace depth contours that completely characterize the response's conditional distributions. Bahadur representation and asymptotic normality results are established. Illustrations are provided both on simulated and real data. © 2015 ISI/BS.
| Original language | English |
|---|---|
| Pages (from-to) | 1435-1466 |
| Journal | Bernoulli |
| Volume | 21 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Aug 2015 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- Conditional depth
- Growth chart
- Halfspace depth
- Local bilinear regression
- Multivariate quantile
- Quantile regression
- Regression depth