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Adaptive estimation of the rank of the regression coefficient matrix

Presented by: 
Marten Herman Wegkamp
Date: 
Tuesday 26th June 2018 - 14:00 to 14:45
Venue: 
INI Seminar Room 1
Abstract: 
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 criterion does not require estimation of the unknown variance of the noise, nor depends on a delicate choice of a tuning parameter. We develop an iterative, fully data-driven procedure, that adapts to the optimal signal-to-noise ratio. This procedure finds the true rank in a few steps with overwhelming probability. At each step, our estimate increases, while at the 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 responses and of covariates grow much faster than the number of observations. An extensive simulation study that confirms our theoretical findings in both low and high dimensional settings. This is joint work with Xin Bing.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons