In this paper, some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high\|dimensional distribution. The limiting d...In this paper, some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high\|dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.展开更多
In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting d...In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated.Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.展开更多
Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution.The limiting distribut...Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution.The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative.The asymptotic properties of bootstrap approximation are investigated.Furthermore,for computational reasons,an approximation for the statistics,based on the number theoretic method,is suggested.展开更多
With the development of the smart grid,the distribution system operation conditions become more complex and changeable.Furthermore,due to the influence of observation outliers and uncertain noise statistics,it is more...With the development of the smart grid,the distribution system operation conditions become more complex and changeable.Furthermore,due to the influence of observation outliers and uncertain noise statistics,it is more difficult to grasp the dynamic operation characteristics of distribution system.In order to address these problems,by using projection statistics and the noise covariance updating technology based on the Sage-Husa noise estimator,for distribution power system with outliers and uncertain noise statistics,a robust adaptive cubature Kalman filter forecasting-aided state estimation method is proposed based on generalized-maximum likelihood type estimator.Furthermore,an adaptive strategy,which can enhance the filtering accuracy under normal conditions,is presented.In the simulation part,the branch parameters and node load parameters of the test system are appropriately modified to simulate the asymmetry of the three-phase branch parameters and the asymmetry of the three-phase loads.Finally,through simulation experiments on the improved test system,it is verified that the robust forecasting-aided state estimation method,presented in this paper,can effectively perceive the actual operating state of the distribution network in different simulation scenarios.展开更多
文摘In this paper, some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high\|dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.
基金the State Education Commission for ReturnedScholar and the NSF or China.
文摘In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated.Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.
文摘Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution.The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative.The asymptotic properties of bootstrap approximation are investigated.Furthermore,for computational reasons,an approximation for the statistics,based on the number theoretic method,is suggested.
基金partially supported by the National Natural Science Foundation of China under Grant 62073121partially supported by National Natural Science Foundation of China-State Grid Joint Fund for Smart Grid under Grant U1966202partially supported by Six Talent Peaks High Level Project of Jiangsu Province under Grant 2017-XNY-004.
文摘With the development of the smart grid,the distribution system operation conditions become more complex and changeable.Furthermore,due to the influence of observation outliers and uncertain noise statistics,it is more difficult to grasp the dynamic operation characteristics of distribution system.In order to address these problems,by using projection statistics and the noise covariance updating technology based on the Sage-Husa noise estimator,for distribution power system with outliers and uncertain noise statistics,a robust adaptive cubature Kalman filter forecasting-aided state estimation method is proposed based on generalized-maximum likelihood type estimator.Furthermore,an adaptive strategy,which can enhance the filtering accuracy under normal conditions,is presented.In the simulation part,the branch parameters and node load parameters of the test system are appropriately modified to simulate the asymmetry of the three-phase branch parameters and the asymmetry of the three-phase loads.Finally,through simulation experiments on the improved test system,it is verified that the robust forecasting-aided state estimation method,presented in this paper,can effectively perceive the actual operating state of the distribution network in different simulation scenarios.
