Abstract
In applications involving, e.g., panel data, images, genomics microarrays, etc., trace regression models are useful tools. To address the high-dimensional issue of these applications, it is common to assume some sparsity property. For the case of the parameter matrix being simultaneously low rank and elements-wise sparse, we estimate the parameter matrix through the least-squares approach with the composite penalty combining the nuclear norm and the l1 norm. We extend the existing analysis of the low-rank trace regression with i.i.d. errors to exponential β-mixing errors. The explicit convergence rate and the asymptotic properties of the proposed estimator are established. Simulations, as well as a real data application, are also carried out for illustration.
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Peng’s research was supported by the NSF of China (Grant No. 12201259), Jiangxi Provincial NSF (Grant No. 20224BAB211008), Science and Technology research project of the Education Department of Jiangxi Province (Grant No. GJJ2200537), Liu’s research was supported by NSF of China (Grant No. 11971208) and NSSF of China (Grant No. 21&ZD152); Tan’s research was supported by the NSF of China (Grant No. 12201260), and NSSF of China (Grant No. 20BTJ008), Science and Technology Research Project of the Education Department of Jiangxi Province (Grant No. GJJ200545), Jiangxi Provincial NSF (Grant No. 20212BAB211010), and China Postdoctoral Science Foundation (Grant No. 2022M711425)
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Peng, L., Tan, X.Y., Xiao, P.W. et al. Oracle Inequality for Sparse Trace Regression Models with Exponential β-mixing Errors. Acta. Math. Sin.-English Ser. 39, 2031–2053 (2023). https://doi.org/10.1007/s10114-023-2153-3
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DOI: https://doi.org/10.1007/s10114-023-2153-3