{"title":"Oracle Inequality for Sparse Trace Regression Models with Exponential β-mixing Errors","authors":"Ling Peng, Xiang Yong Tan, Pei Wen Xiao, Zeinab Rizk, Xiao Hui Liu","doi":"10.1007/s10114-023-2153-3","DOIUrl":null,"url":null,"abstract":"<div><p>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 <i>l</i><sub>1</sub> norm. We extend the existing analysis of the low-rank trace regression with i.i.d. errors to exponential <i>β</i>-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.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-2153-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.