This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectatio...This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.展开更多
We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisen- berg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau...We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisen- berg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers S. The values of the critical mag- netic fields and the widths of the magnetization plateaus are fully consistent with the recent numerical results from exact diagonalization and infinite projected entangled paired states.展开更多
This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential o...This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the inte展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.11271014 and 11971045。
文摘This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10934008,10874215 and 11174365the National Basic Research Program of China under Grant Nos 2012CB921704 and 2011CB309703
文摘We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisen- berg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers S. The values of the critical mag- netic fields and the widths of the magnetization plateaus are fully consistent with the recent numerical results from exact diagonalization and infinite projected entangled paired states.
文摘This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the inte
