Detecting differential expression of genes in genom research(e.g.,2019-nCoV)is not uncommon,due to the cost only small sample is employed to estimate a large number of variances(or their inverse)of variables simultane...Detecting differential expression of genes in genom research(e.g.,2019-nCoV)is not uncommon,due to the cost only small sample is employed to estimate a large number of variances(or their inverse)of variables simultaneously.However,the commonly used approaches perform unreliable.Borrowing information across different variables or priori information of variables,shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic.In this paper,we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution.Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well.In addition,application comparison and real data analysis indicate that the proposed estimator also works well.展开更多
Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both D...Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold.In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.展开更多
基金Supported by the National Natural Science Foundation of China(11971433)First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)Hunan Soft Science Research Project(2012ZK3064)
文摘Detecting differential expression of genes in genom research(e.g.,2019-nCoV)is not uncommon,due to the cost only small sample is employed to estimate a large number of variances(or their inverse)of variables simultaneously.However,the commonly used approaches perform unreliable.Borrowing information across different variables or priori information of variables,shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic.In this paper,we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution.Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well.In addition,application comparison and real data analysis indicate that the proposed estimator also works well.
文摘Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold.In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.
