Adaptive estimation of the rank of the regression coefficient matrix
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About this item
| Description: |
Wegkamp, M
Tuesday 26th June 2018 - 14:00 to 14:45 |
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| Created: | 2018-06-27 14:52 |
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| Collection: | Statistical scalability |
| Publisher: | Isaac Newton Institute |
| Copyright: | Wegkamp, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| 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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