Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclus...Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclusion region for tensors is established. It is proved that the new eigenvalue inclusion region is tighter than that of Y. Yang and Q. Yang [SIAM J. Matrix Anal. Appl., 2010, 31： 2517-2530]. Numerical examples are reported to demonstrate the corresponding results.展开更多
The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect ag...The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as ＇weighted estimating equations （WEE）＇ for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11361074, 11326242） and the Science Foundation of the Education Department of Yunnan Province （Grant No. 2013FD002）.
文摘Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclusion region for tensors is established. It is proved that the new eigenvalue inclusion region is tighter than that of Y. Yang and Q. Yang [SIAM J. Matrix Anal. Appl., 2010, 31： 2517-2530]. Numerical examples are reported to demonstrate the corresponding results.
文摘The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as ＇weighted estimating equations （WEE）＇ for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.
