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SUMMARY:Adaptive estimation of the rank of the regression coefficient matr
 ix - Marten Herman Wegkamp (Cornell University)
DTSTART:20180626T130000Z
DTEND:20180626T134500Z
UID:TALK107404@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider the multivariate response regression problem with 
 a regression coefficient matrix of  low\, unknown rank. In this setting\, 
 we analyze a new criterion for selecting the optimal reduced rank. This cr
 iterion does not require  estimation of the unknown variance of the noise\
 , nor depends on a delicate choice of a tuning parameter. We develop an it
 erative\, fully data-driven procedure\, that adapts to the optimal signal-
 to-noise ratio. This procedure finds the true rank in a few steps with ove
 rwhelming probability. At each step\, our estimate increases\, while at th
 e same time  it does not exceed the true rank. Our finite sample results  
 hold for any sample size and any dimension\, even when the number of respo
 nses and of covariates grow much faster than the number of observations. A
 n extensive simulation study that confirms our theoretical findings in bot
 h low and high dimensional settings. This is joint work with Xin Bing.
LOCATION:Seminar Room 1\, Newton Institute
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