Bibliographic Details
| Title: |
Sparse Reduced Rank Huber Regression in High Dimensions. |
| Authors: |
Tan, Kean Ming1 (AUTHOR), Sun, Qiang2 (AUTHOR) qiang.sun@utoronto.ca, Witten, Daniela3 (AUTHOR) |
| Superior Title: |
Journal of the American Statistical Association. Dec2023, Vol. 118 Issue 544, p2383-2393. 11p. |
| Subject Terms: |
STATISTICAL bias, RANDOM noise theory |
| Abstract: |
We propose a sparse reduced rank Huber regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained nonconvex optimization problem, which is then solved using a block coordinate descent and an alternating direction method of multipliers algorithm. We establish nonasymptotic estimation error bounds under both Frobenius and nuclear norms in the high-dimensional setting. This is a major contribution over existing results in reduced rank regression, which mainly focus on rank selection and prediction consistency. Our theoretical results quantify the tradeoff between heavy-tailedness of the random noise and statistical bias. For random noise with bounded (1 + δ) th moment with δ ∈ (0 , 1) , the rate of convergence is a function of δ, and is slower than the sub-Gaussian-type deviation bounds; for random noise with bounded second moment, we obtain a rate of convergence as if sub-Gaussian noise were assumed. We illustrate the performance of the proposed method via extensive numerical studies and a data application. for this article are available online. [ABSTRACT FROM AUTHOR] |
|
Copyright of Journal of the American Statistical Association is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Business Source Premier |
