We prove that the inequality m+n/mn+min{m,n}≤m m∑i=1（n∑j=1xij）^2+n n∑j=1（m∑i=1xij）^2/（m∑i=1 n∑j=1xij）^2+mn m∑i=1 n∑j=1x^2ij holds, when a m×n real matrix X = (xij) whose entries are not all equal t...We prove that the inequality m+n/mn+min{m,n}≤m m∑i=1（n∑j=1xij）^2+n n∑j=1（m∑i=1xij）^2/（m∑i=1 n∑j=1xij）^2+mn m∑i=1 n∑j=1x^2ij holds, when a m×n real matrix X = (xij) whose entries are not all equal to 0 satisfies txX^TX}≤min{m∑i=1（n∑j=1xij）^2，n∑j=1（m∑i=1xij）^2}.Therefore we not only generalize the results of Horst Alzer [2] from non-negative matrix to real matrix, but also complete a result of E R van Dam [1], which indicated that the best possible upper bound is equal to 1 for real matrix.展开更多
In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
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 prop...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 l1norm.We extend the existing analysis of the low-rank trace regression with i.i.d.errors to exponentialβ-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.展开更多
基金Supported by the Science Foundation of Educational Commission of Fujian Province (JA03157)Supported by the Scientific Research Item of Putian University(20042002)
文摘We prove that the inequality m+n/mn+min{m,n}≤m m∑i=1（n∑j=1xij）^2+n n∑j=1（m∑i=1xij）^2/（m∑i=1 n∑j=1xij）^2+mn m∑i=1 n∑j=1x^2ij holds, when a m×n real matrix X = (xij) whose entries are not all equal to 0 satisfies txX^TX}≤min{m∑i=1（n∑j=1xij）^2，n∑j=1（m∑i=1xij）^2}.Therefore we not only generalize the results of Horst Alzer [2] from non-negative matrix to real matrix, but also complete a result of E R van Dam [1], which indicated that the best possible upper bound is equal to 1 for real matrix.
文摘In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
基金supported by the NSF of China(Grant No.12201259)supported by NSF of China(Grant No.11971208)+7 种基金supported by the NSF of China(Grant No.12201260)Jiangxi Provincial NSF(Grant No.20224BAB211008)Jiangxi Provincial NSF(Grant No.20212BAB211010)Science and Technology research project of the Education Department of Jiangxi Province(Grant No.GJJ2200537)Science and Technology Research Project of the Education Department of Jiangxi Province(Grant No.GJJ200545)NSSF of China(Grant No.21&ZD152)NSSF of China(Grant No.20BTJ008)China Postdoctoral Science Foundation(Grant No.2022M711425)。
文摘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 l1norm.We extend the existing analysis of the low-rank trace regression with i.i.d.errors to exponentialβ-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.
