Expectile trace regression via low-rank and group sparsity regularization

AbstractTrace regression has received a lot of attention due to its ability to account for matrix-type covariates, including panel data, images, and genomic microarrays as special cases. However, most of its existing research focuses on the case of mean regression. In this paper, we consider the expectile trace regression, which can provide a more diversified picture of the regression relationship at different expectiles, via the low-rank and group sparsity regularization. The upper bound for the statistical rate of convergence of the regularized estimator is established under some mild conditions. Some simulations, as well as a real data example, are also provided to illustrate the finite sample performance of the developed expectile trace regression.Keywords: Expectile trace regressionlow-rankupper boundconvergence ratematrix-type covariates2020 Mathematics Subject Classifications: 62J9962H12 AcknowledgementsThe authors thank one anonymous referee and the associate editor for their valuable comments, which have led to many improvements to this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingLing Peng's research was supported by the NSF of China (Grant No. 12201259), Jiangxi Provincial NSF (Grant No. 20224BAB211008), and the Science & Technology research project of the Education Department of Jiangxi Province (Grant No. GJJ2200537). Xiangyong Tan's research was supported by the NSF of China (Grant No. 12201260), Jiangxi Provincial NSF (Grant No. 20212BAB211010), and China Postdoctoral Science Foundation (2022M711425). Xiaohui Liu's research is supported by NSF of China (Grant No. 11971208), the National Social Science Foundation of China (21&ZD152), and the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province (No. 20224ACB211003).