By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
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
Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As app...Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.展开更多
In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the p...In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.展开更多
We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend...We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.展开更多
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
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.
基金the National Natural Science Fbundation of China (Grant Nos. 10161004, 70221001, 70331001)the Natural Science Foundation of Guangxi Province of China (Grant No. 04047033)
文摘Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11671012,11871072,11701004,11701005)the Natural Science Foundation of Anhui Province(Nos.1808085QA03,1908085QA01,1908085QA07)and the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003).
文摘In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.
基金Acknowledgements The authors would like to express their sincere gratitude to the two anonymous referees for their value comments and suggestions. This work was supported by the National Natural Science Foundation of China （Grant Nos. 61272023, 61101240）.
文摘We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.
