• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.371-382
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• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.429-441
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• 2014

In this work we study two a posteriori error estimators of hierarchical type for lowest-order mixed finite element methods. One estimator is computed by solving a global defect problem based on the splitting of the lowest-order Brezzi-Douglas-Marini space, and the other estimator is locally computable by applying the standard localization to the first estimator. We establish the reliability and efficiency of both estimators by comparing them with the standard residual estimator. In addition, it is shown that the error estimator based on the global defect problem is asymptotically exact under suitable conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.1-13
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• 2012

In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.

• Journal of KSNVE
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• v.9 no.6
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• pp.1240-1246
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• 1999

A prior error estimator which is solving structural dynamic problems and which is based on the generalized-method, is developed. Since the proposed error estimator is computed with only previous information, the time step size can be adaptively selected without the feedback mechanism. This paper shows that the automatic time stepping algorithm using the error estimator performs an efficient time integration. To verify its efficiency, several examples are numerically investigated.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.293-304
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• 2013

In this paper we analyze an error estimator for the lowest-order triangular Raviart-Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385{395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.1-8
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• 1996

A new error measure for a static finite element analysis is proposed. This error measure is a modification to the Zienkiewicz and Zhu energy norm. The new error estimator is a global error measure for the analysis and is independent of finite element model size and internal stresses, hence it is readily transportable to other error calculations. It is shown in this paper the the new error estimator also produces conservative error measurements, making it a suitable procedure to adopt in commerical packages.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.115-134
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• 1994

Polynomial errors-in-variables model with one predictor variable and one response variable is defined and an estimator of model is derived following the Booth's linear model estimation procedure. Since polynomial model is nonlinear function of the unknown regression coefficients and error-free predictors, it is nonlinear model in errors-in-variables model. As a result of applying linear model estimation method to nonlinear model, some additional assumptions are necessary. Hence, an estimator is derived under the assumption that the error variances are decrasing as sample size increases. Asymptotic propoerties of the derived estimator are provided. A simulation study is presented to compare the small sample properties of the derived estimator with those of OLS estimator.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.137-150
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• 2016

In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and $Verf{\ddot{u}}rth$ based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.501-508
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• 2003

Although the estimate of regression function is important, some have focused the variance estimation of error term in regression model. Different variance estimators perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are approximately satisfied so as to identify the best variance estimator for the given data. In this article, we suggest SHM estimator compared to LS estimator, which is common estimator using in parametric multiple regression analysis. Moreover, a combined estimator of variance, VEM, is suggested. In the simulation study it is shown that VEM performs well in practice.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.393-406
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• 2020

We analyze a posteriori error estimator for the conforming P2 finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming P1 finite element proposed in [4]. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.