In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matchi...The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.展开更多
Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper.The method is based on equivalent first order system of the elliptic problem and rectangle-triangle trans...Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper.The method is based on equivalent first order system of the elliptic problem and rectangle-triangle transforms.It fully enjoys the ten-sorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh.Different from the usual Galerkin formulation,the mixed form is particularly advantageous in this context,since it can avoid the singularity in-duced by the rectangle-triangle transform in the calculation of the matrices,and does not require the evaluation of the stiffness matrix.An hp a priori error estimate is pres-ented for the proposed method.The implementation details and some numerical exam-ples are provided to validate the accuracy and flexibility of the method.展开更多
Probabilistic load forecasting(PLF)is able to present the uncertainty information of the future loads.It is the basis of stochastic power system planning and operation.Recent works on PLF mainly focus on how to develo...Probabilistic load forecasting(PLF)is able to present the uncertainty information of the future loads.It is the basis of stochastic power system planning and operation.Recent works on PLF mainly focus on how to develop and combine forecasting models,while the feature selection issue has not been thoroughly investigated for PLF.This paper fills the gap by proposing a feature selection method for PLF via sparse L1-norm penalized quantile regression.It can be viewed as an extension from point forecasting-based feature selection to probabilistic forecasting-based feature selection.Since both the number of training samples and the number of features to be selected are very large,the feature selection process is casted as a large-scale convex optimization problem.The alternating direction method of multipliers is applied to solve the problem in an efficient manner.We conduct case studies on the open datasets of ten areas.Numerical results show that the proposed feature selection method can improve the performance of the probabilistic forecasting and outperforms traditional least absolute shrinkage and selection operator method.展开更多
基金Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金This work was subsidized by the special funds for major state basic research projects under 2005CB321700 and a grant from the National Science Foundation （NSF） of China （No. 10471144）.
文摘The mortar element method is a new domain decomposition method（DDM） with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H^1-norm estimates are obtained under a reasonable elliptic regularity assumption.
基金The first and second authors gratefully acknowledge the financial support provided by NSFC(grant 11771137)。
文摘Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper.The method is based on equivalent first order system of the elliptic problem and rectangle-triangle transforms.It fully enjoys the ten-sorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh.Different from the usual Galerkin formulation,the mixed form is particularly advantageous in this context,since it can avoid the singularity in-duced by the rectangle-triangle transform in the calculation of the matrices,and does not require the evaluation of the stiffness matrix.An hp a priori error estimate is pres-ented for the proposed method.The implementation details and some numerical exam-ples are provided to validate the accuracy and flexibility of the method.
基金supported by National Key R&D Program of China(No.2016YFB0900100).
文摘Probabilistic load forecasting(PLF)is able to present the uncertainty information of the future loads.It is the basis of stochastic power system planning and operation.Recent works on PLF mainly focus on how to develop and combine forecasting models,while the feature selection issue has not been thoroughly investigated for PLF.This paper fills the gap by proposing a feature selection method for PLF via sparse L1-norm penalized quantile regression.It can be viewed as an extension from point forecasting-based feature selection to probabilistic forecasting-based feature selection.Since both the number of training samples and the number of features to be selected are very large,the feature selection process is casted as a large-scale convex optimization problem.The alternating direction method of multipliers is applied to solve the problem in an efficient manner.We conduct case studies on the open datasets of ten areas.Numerical results show that the proposed feature selection method can improve the performance of the probabilistic forecasting and outperforms traditional least absolute shrinkage and selection operator method.
