BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Least squares estimation: Beyond Gaussian regression models - Qiya
 ng Han (University of Washington)
DTSTART:20180508T100000Z
DTEND:20180508T110000Z
UID:TALK105241@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We study the convergence rate of the least squares estimator (
 LSE) in a regression model with possibly heavy-tailed errors. Despite its 
 importance in practical applications\, theoretical understanding of this p
 roblem has been limited. We first show that from a worst-case perspective\
 , the convergence rate of the LSE in a general non-parametric regression m
 odel is given by the maximum of the Gaussian regression rate and the noise
  rate induced by the errors. In the more difficult statistical model where
  the errors only have a second moment\, we further show that the sizes of 
 the &#39\;localized envelopes&#39\; of the model give a sharp interpolatio
 n for the convergence rate of the LSE between the worst-case rate and the 
 (optimal) parametric rate. These results indicate both certain positive an
 d negative aspects of the LSE as an estimation procedure in a heavy-tailed
  regression setting.&nbsp\;The key technical innovation is a new multiplie
 r inequality that sharply controls the size of the multiplier empirical pr
 ocess associated with the LSE\, which also finds applications in shape-res
 tricted and sparse linear regression problems.  <br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR