Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid...Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.展开更多
Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which ...Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.展开更多
The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed e...The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.展开更多
In this paper, we have proposed an estimator of finite population mean using a new regression type estimator with two auxiliary variables for single-phase sampling and investigated its finite sample properties. An emp...In this paper, we have proposed an estimator of finite population mean using a new regression type estimator with two auxiliary variables for single-phase sampling and investigated its finite sample properties. An empirical study has been carried out to compare the performance of the proposed estimator with the existing estimators that utilize auxiliary variables for finite population mean. It has been found that the new regression type estimator with two auxiliary variables for to be more efficient than mean per unit, ratio and product estimator and exponential ratio and exponential product estimators and exponential ratio-product estimator.展开更多
In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likeliho...In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.展开更多
In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared w...In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc. Finally, a numerical example and a Monte Carlo simulation are given to explain some of the theoretical results.展开更多
This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple e...This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple exponential distributions, with a different parameter for each patient. The analyses are carried out in case of progressive censoring assuming squared error loss function and gamma distribution as priors and hyperpriors. The possibilities of using the methodology in more general situations like dose- response modeling have also been explored. Bayesian estimators derived in this paper are applied to lung cancer data set with concomitant variables.展开更多
In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearit...In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.展开更多
Digital elevation model(DEM)matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator,in which terrain changes are treated as gross errors.H...Digital elevation model(DEM)matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator,in which terrain changes are treated as gross errors.However,all existing methods only emphasise their deformation detecting ability,and neglect another important aspect:only when the gross error can be detected and located,can this system be useful.This paper employs the gross error judgement matrix as a tool to make an in-depth analysis of this problem.The theoretical analyses and experimental results show that observations in the DEM matching algorithm in real applications have the ability to detect and locate gross errors.Therefore,treating the terrain changes as gross errors is theoretically feasible,allowing real DEM deformations to be detected by employing a surface matching technique.展开更多
This paper considers the semiparametric regression model Yi = xiβ＋g（ti）＋ Vi （1 ≤ i≤ n）, where （xi, ti） are known design points, fl is an unknown slope parameter, g（.） is an unknown function, the correlate...This paper considers the semiparametric regression model Yi = xiβ＋g（ti）＋ Vi （1 ≤ i≤ n）, where （xi, ti） are known design points, fl is an unknown slope parameter, g（.） is an unknown function, the correlated errors Vi = ∑^∞j=-∞cjei-j with ∑^∞j=-∞｜cj｜ 〈 ∞, and ei are negatively associated random variables. Under appropriate conditions, the authors study the asymptotic normality for wavelet estimators ofβ and g（·）. A simulation study is undertaken to investigate finite sample behavior of the estimators.展开更多
Wavelet analysis is one of the mostly new methods of pure and applied mathematics science. In this paper, we use the wavelet method to estimate the hazard function for censoring random variable. We consider the conver...Wavelet analysis is one of the mostly new methods of pure and applied mathematics science. In this paper, we use the wavelet method to estimate the hazard function for censoring random variable. We consider the convergence ratio of given estimator. Also we present the simulation in order to test purpose estimator by calculating the mean integrated squared error (MISE) and average mean squared error (AMSE).展开更多
Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive r...Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.展开更多
Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a La...Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution.Large sample properties,including the consistency and the asymptotic normality,are investigated.The finite sample performance of the proposed estimators are evaluated via simulation studies,as well as comparison studies with some existing estimation procedures.展开更多
基金Projects(2006AA06Z105, 2007AA06Z134) supported by the National High-Tech Research and Development Program of ChinaProjects(2007, 2008) supported by China Scholarship Council (CSC)
文摘Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.
基金the National Natural Science Foundation of China(Grant No.10771150)the National Basic Research Program of China(Grant No.2005CB321701)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0584)
文摘Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.
文摘The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.
文摘In this paper, we have proposed an estimator of finite population mean using a new regression type estimator with two auxiliary variables for single-phase sampling and investigated its finite sample properties. An empirical study has been carried out to compare the performance of the proposed estimator with the existing estimators that utilize auxiliary variables for finite population mean. It has been found that the new regression type estimator with two auxiliary variables for to be more efficient than mean per unit, ratio and product estimator and exponential ratio and exponential product estimators and exponential ratio-product estimator.
文摘In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.
文摘In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc. Finally, a numerical example and a Monte Carlo simulation are given to explain some of the theoretical results.
文摘This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple exponential distributions, with a different parameter for each patient. The analyses are carried out in case of progressive censoring assuming squared error loss function and gamma distribution as priors and hyperpriors. The possibilities of using the methodology in more general situations like dose- response modeling have also been explored. Bayesian estimators derived in this paper are applied to lung cancer data set with concomitant variables.
文摘In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.
基金This research is supported by the National High Technology Plan(863)of the People’s Republic of China,Project No.2009AA12Z207.
文摘Digital elevation model(DEM)matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator,in which terrain changes are treated as gross errors.However,all existing methods only emphasise their deformation detecting ability,and neglect another important aspect:only when the gross error can be detected and located,can this system be useful.This paper employs the gross error judgement matrix as a tool to make an in-depth analysis of this problem.The theoretical analyses and experimental results show that observations in the DEM matching algorithm in real applications have the ability to detect and locate gross errors.Therefore,treating the terrain changes as gross errors is theoretically feasible,allowing real DEM deformations to be detected by employing a surface matching technique.
基金supported by the National Natural Science Foundation of China under Grant No.10871146
文摘This paper considers the semiparametric regression model Yi = xiβ＋g（ti）＋ Vi （1 ≤ i≤ n）, where （xi, ti） are known design points, fl is an unknown slope parameter, g（.） is an unknown function, the correlated errors Vi = ∑^∞j=-∞cjei-j with ∑^∞j=-∞｜cj｜ 〈 ∞, and ei are negatively associated random variables. Under appropriate conditions, the authors study the asymptotic normality for wavelet estimators ofβ and g（·）. A simulation study is undertaken to investigate finite sample behavior of the estimators.
文摘Wavelet analysis is one of the mostly new methods of pure and applied mathematics science. In this paper, we use the wavelet method to estimate the hazard function for censoring random variable. We consider the convergence ratio of given estimator. Also we present the simulation in order to test purpose estimator by calculating the mean integrated squared error (MISE) and average mean squared error (AMSE).
文摘Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.
基金supported by the National Science Foundation of Shanxi Province of China under Grant No.2013011002-1supported by the Division of Mathematical Science,National Science Foundation under Grant No.1205276
文摘Based on a Tweedie-type formula developed under the Laplace distribution,this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution.Large sample properties,including the consistency and the asymptotic normality,are investigated.The finite sample performance of the proposed estimators are evaluated via simulation studies,as well as comparison studies with some existing estimation procedures.
