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SUMMARY:Local Bilinear Multiple-Output Quantile Regression: from $L_1$ Opt
 imization to Regression Depth - Marc Hallin\, ECARES\, Universite libre de
  Bruxelles and ORFE\, Princeton University
DTSTART:20130208T160000Z
DTEND:20130208T170000Z
UID:TALK42436@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:A new multiple output concept of quantile regression\, based o
 n a directional\nversion of Koenker and Bassett?s traditional one\, has be
 en introduced in\nHallin\, Paindaveine and Siman (Annals of Statistics 201
 0\, 635-703)\,\nessentially for multivariate location problems. The empiri
 cal counterpart of\nthat concept produces polyhedral contours that (in the
  location case)\ncoincide with the Tukey halfspace depth contours. In a re
 gression context\,\nhowever\, that concept cannot account for nonlinear or
 /and heteroscedastic\ndependencies. A local bilinear version of those cont
 ours is proposed here\,\nwhich asymptotically recovers the conditional hal
 fspace depth contours of\nthe multiple-output response. A Bahadur represen
 tation is established\, along\nwith asymptotic normality results. Examples
  are provided.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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