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Article
Publication date: 1 May 1995

L. Fourment and J.L. Chenot

The analysis of error estimation is addressed in the framework ofviscoplasticity problems, this is to say, of incompressible andnon‐linear materials. Firstly…

Abstract

The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z2) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L2 and Lnorms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

Details

Engineering Computations, vol. 12 no. 5
Type: Research Article
ISSN: 0264-4401

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Book part
Publication date: 12 December 2003

R.Carter Hill, Lee C. Adkins and Keith A. Bender

The Heckman two-step estimator (Heckit) for the selectivity model is widely applied in Economics and other social sciences. In this model a non-zero outcome variable is…

Abstract

The Heckman two-step estimator (Heckit) for the selectivity model is widely applied in Economics and other social sciences. In this model a non-zero outcome variable is observed only if a latent variable is positive. The asymptotic covariance matrix for a two-step estimation procedure must account for the estimation error introduced in the first stage. We examine the finite sample size of tests based on alternative covariance matrix estimators. We do so by using Monte Carlo experiments to evaluate bootstrap generated critical values and critical values based on asymptotic theory.

Details

Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later
Type: Book
ISBN: 978-1-84950-253-5

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Book part
Publication date: 23 November 2011

Daniel L. Millimet

Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such…

Abstract

Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such effects are divided into one of two strands depending on whether they require unconfoundedness (i.e., independence of potential outcomes and treatment assignment conditional on a set of observable covariates). When this assumption holds, researchers now have a wide array of estimation techniques from which to choose. However, very little is known about their performance – both in absolute and relative terms – when measurement error is present. In this study, the performance of several estimators that require unconfoundedness, as well as some that do not, are evaluated in a Monte Carlo study. In all cases, the data-generating process is such that unconfoundedness holds with the ‘real’ data. However, measurement error is then introduced. Specifically, three types of measurement error are considered: (i) errors in treatment assignment, (ii) errors in the outcome, and (iii) errors in the vector of covariates. Recommendations for researchers are provided.

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Missing Data Methods: Cross-sectional Methods and Applications
Type: Book
ISBN: 978-1-78052-525-9

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Article
Publication date: 2 March 2015

Michael Bleaney and Zhiyong Li

This paper aims to investigate the performance of estimators of the bid-ask spread in a wide range of circumstances and sampling frequencies. The bid-ask spread is…

Abstract

Purpose

This paper aims to investigate the performance of estimators of the bid-ask spread in a wide range of circumstances and sampling frequencies. The bid-ask spread is important for many reasons. Because spread data are not always available, many methods have been suggested for estimating the spread. Existing papers focus on the performance of the estimators either under ideal conditions or in real data. The gap between ideal conditions and the properties of real data are usually ignored. The consistency of the estimates across various sampling frequencies is also ignored.

Design/methodology/approach

The estimators and the possible errors are analysed theoretically. Then we perform simulation experiments, reporting the bias, standard deviation and root mean square estimation error of each estimator. More specifically, we assess the effects of the following factors on the performance of the estimators: the magnitude of the spread relative to returns volatility, randomly varying of spreads, the autocorrelation of mid-price returns and mid-price changes caused by trade directions and feedback trading.

Findings

The best estimates come from using the highest frequency of data available. The relative performance of estimators can vary quite markedly with the sampling frequency. In small samples, the standard deviation can be more important to the estimation error than bias; in large samples, the opposite tends to be true.

Originality/value

There is a conspicuous lack of simulation evidence on the comparative performance of different estimators of the spread under the less than ideal conditions that are typical of real-world data. This paper aims to fill this gap.

Details

Studies in Economics and Finance, vol. 32 no. 1
Type: Research Article
ISSN: 1086-7376

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Article
Publication date: 1 September 2002

Ch. Pinto, R. Avilés, J. Albizuri and A. Hernández

In this second part of the paper, some properties of the discretization error estimators are presented, although their theoretical background was already developed in the…

Abstract

In this second part of the paper, some properties of the discretization error estimators are presented, although their theoretical background was already developed in the first part. Two numerical examples have been selected and will be used to check some properties of these error estimators. In addition to this, some practical conclusions will be addressed from the results and graphical output of the implemented procedure.

Details

Engineering Computations, vol. 19 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 5 July 2013

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creuse, Serge Nicaise, Francis Piriou and Nicolas Nemitz

In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a…

Abstract

Purpose

In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation.

Design/methodology/approach

The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency).

Findings

This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation.

Originality/value

In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 May 2000

A. Rieger and P. Wriggers

Several a posteriori error indicators and error estimators for frictionless contact problems are compared. In detail, residual based error estimators, error indicators…

Abstract

Several a posteriori error indicators and error estimators for frictionless contact problems are compared. In detail, residual based error estimators, error indicators relying on superconvergence properties and error estimators based on duality principles are investigated. Applications are to 2D solids under the hypothesis of nonlinear elastic material behaviour associated with finite deformations. A penalization technique is applied to enforce multilateral boundary conditions due to contact. The approximate solution of the problem is obtained by using the finite element method. Several numerical results are reported to show the applicability of the adaptive algorithm to the considered problems.

Details

Engineering Computations, vol. 17 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 May 2002

D.H. Wu and I.G. Currie

An à‐posteriori error indicator for solving viscous incompressible flow problems is analyzed in this paper. The indicator named “velocity angle error estimator” is based…

Abstract

An à‐posteriori error indicator for solving viscous incompressible flow problems is analyzed in this paper. The indicator named “velocity angle error estimator” is based on the spatial derivative of velocity direction fields and it can detect local flow features, such as vortices and separation, and resolve flow details precisely. The refinement indicator corresponds to the antisymmetric part of the deformation‐rate‐tensor, and it is sensitive to the second derivative of the velocity angle field. Rationality discussions reveal that the à‐posteriori error indicator is a curvature error indicator, and its value reflects the accuracy of streamline curves. It is also found that the velocity angle error indicator contains the nonlinear convective term of the Navier–Stokes equations, and it identifies and computes the direction difference when the convective acceleration direction and the flow velocity direction have a disparity. Numerical simulation is presented to illustrate the use of the velocity angle error indicator.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 3
Type: Research Article
ISSN: 0961-5539

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Book part
Publication date: 12 December 2003

Badi H. Baltagi, Georges Bresson and Alain Pirotte

In the spirit of White’s (1982) paper, this paper examines the consequences of model misspecification using a panel data regression model. Maximum likelihood, random and…

Abstract

In the spirit of White’s (1982) paper, this paper examines the consequences of model misspecification using a panel data regression model. Maximum likelihood, random and fixed effects estimators are compared using Monte Carlo experiments under normality of the disturbances but with a possibly misspecified variance-covariance matrix. We show that the correct GLS (ML) procedure is always the best according to MSE performance, but the researcher does not have perfect foresight on the true form of the variance covariance matrix. In this case, we show that a pretest estimator is a viable alternative given that its performance is a close second to correct GLS (ML) whether the true specification is a two-way, a one-way error component model or a pooled regression model. Incorrect GLS, ML or fixed effects estimators may lead to a big loss in MSE.

Details

Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later
Type: Book
ISBN: 978-1-84950-253-5

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Article
Publication date: 9 November 2012

Octavio Andrés González‐Estrada, Juan José Ródenas, Stéphane Pierre Alain Bordas, Marc Duflot, Pierre Kerfriden and Eugenio Giner

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the…

Abstract

Purpose

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).

Design/methodology/approach

The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.

Findings

Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.

Originality/value

The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.

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