Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are ...Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.展开更多
In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an au...In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.展开更多
In this paper,we investigate initial boundary value problems of the spacetime fractional diffusion equation and its numerical solutions.Two definitions,i.e.,Riemann-Liouville definition and Caputo one,of the fractiona...In this paper,we investigate initial boundary value problems of the spacetime fractional diffusion equation and its numerical solutions.Two definitions,i.e.,Riemann-Liouville definition and Caputo one,of the fractional derivative are considered in parallel.In both cases,we establish the well-posedness of the weak solution.Moveover,based on the proposed weak formulation,we construct an efficient spectral method for numerical approximations of the weak solution.The main contribution of this work are threefold:First,a theoretical framework for the variational solutions of the space-time fractional diffusion equation is developed.We find suitable functional spaces and norms in which the space-time fractional diffusion problem can be formulated into an elliptic weak problem,and the existence and uniqueness of the weak solution are then proved by using existing theory for elliptic problems.Secondly,we show that in the case of Riemann-Liouville definition,the well-posedness of the space-time fractional diffusion equation does not require any initial conditions.This contrasts with the case of Caputo definition,in which the initial condition has to be integrated into the weak formulation in order to establish the well-posedness.Finally,thanks to the weak formulation,we are able to construct an efficient numerical method for solving the space-time fractional diffusion problem.展开更多
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also o...Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required;this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example. A listing of open-source software is provided in the Appendix.展开更多
It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference ...Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.展开更多
In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple ...In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple computational manner to obtain a quite acceptable approximate solution.The main characteristic behind this method lies in the fact that,on the one hand,the problem will be reduced to a system of algebraic equations.On the other hand,the efficiency and accuracy of the Bernstein polynomials method for solving these equations are high.The existence and uniqueness of the solution have been proved.Moreover,an estimation of the error bound for this method will be shown by preparing some theorems.Finally,some numerical experiments are presented to show the excellent behavior and high accuracy of this algorithm in comparison with some other well-known methods.展开更多
In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to ...In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.展开更多
Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables....Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables. In this paper, we adapted this class and motivated by Searle [13], and we suggested more generalized class of estimators for estimating the population variance in simple random sampling. The expressions for the mean square error of proposed class have been derived in general form. Besides obtaining the minimized MSE of the proposed and adapted class, it is shown that the adapted classis the special case of the proposed class. Moreover, these theoretical findings are supported by an empirical study of original data.展开更多
In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least square...In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least squares estimator （LSE） is investigated under the mean square error （MSE） criterion. Finally, some simulation results for the PEBE are obtained.展开更多
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
文摘In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.
文摘In this paper,we investigate initial boundary value problems of the spacetime fractional diffusion equation and its numerical solutions.Two definitions,i.e.,Riemann-Liouville definition and Caputo one,of the fractional derivative are considered in parallel.In both cases,we establish the well-posedness of the weak solution.Moveover,based on the proposed weak formulation,we construct an efficient spectral method for numerical approximations of the weak solution.The main contribution of this work are threefold:First,a theoretical framework for the variational solutions of the space-time fractional diffusion equation is developed.We find suitable functional spaces and norms in which the space-time fractional diffusion problem can be formulated into an elliptic weak problem,and the existence and uniqueness of the weak solution are then proved by using existing theory for elliptic problems.Secondly,we show that in the case of Riemann-Liouville definition,the well-posedness of the space-time fractional diffusion equation does not require any initial conditions.This contrasts with the case of Caputo definition,in which the initial condition has to be integrated into the weak formulation in order to establish the well-posedness.Finally,thanks to the weak formulation,we are able to construct an efficient numerical method for solving the space-time fractional diffusion problem.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
文摘Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required;this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example. A listing of open-source software is provided in the Appendix.
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
文摘Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
基金Supported by the Shiraz University of Technology,Shiraz,Iran.
文摘In this paper,the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with variable coefficients and mixed conditions.This method is using a simple computational manner to obtain a quite acceptable approximate solution.The main characteristic behind this method lies in the fact that,on the one hand,the problem will be reduced to a system of algebraic equations.On the other hand,the efficiency and accuracy of the Bernstein polynomials method for solving these equations are high.The existence and uniqueness of the solution have been proved.Moreover,an estimation of the error bound for this method will be shown by preparing some theorems.Finally,some numerical experiments are presented to show the excellent behavior and high accuracy of this algorithm in comparison with some other well-known methods.
文摘In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.
文摘Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables. In this paper, we adapted this class and motivated by Searle [13], and we suggested more generalized class of estimators for estimating the population variance in simple random sampling. The expressions for the mean square error of proposed class have been derived in general form. Besides obtaining the minimized MSE of the proposed and adapted class, it is shown that the adapted classis the special case of the proposed class. Moreover, these theoretical findings are supported by an empirical study of original data.
文摘In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least squares estimator （LSE） is investigated under the mean square error （MSE） criterion. Finally, some simulation results for the PEBE are obtained.
