In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some sp...The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.展开更多
In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing respo...In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In add...For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated ran...In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.展开更多
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金supported by National Natural Science Foundation of China (Grant Nos. 11401006, 11671299 and 11671042)a grant from the University Grants Council of Hong Kong+1 种基金the China Postdoctoral Science Foundation (Grant No. 2017M611083)the National Statistical Science Research Program of China (Grant No. 2015LY55)
文摘The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.
基金Supported by National Natural Science Foundation of China （Grant No. 10871013）, Natural Science Foundation of Beijing （Grant No. 1072004）, and Natural Science Foundation of Guangxi Province （Grant No. 2010GXNSFB013051）
文摘In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y6090131the Natural Science Foundation of Ningbo City under Grant No.2010A610101
文摘For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.
