Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to ce...

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Main Authors: Ali Erkoc, Esra Emiroglu, Kadri Ulas Akay
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/806471
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author Ali Erkoc
Esra Emiroglu
Kadri Ulas Akay
author_facet Ali Erkoc
Esra Emiroglu
Kadri Ulas Akay
author_sort Ali Erkoc
collection DOAJ
description In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.
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institution Kabale University
issn 2356-6140
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language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series The Scientific World Journal
spelling doaj-art-5bd00af060e54e45be20e7e3129b8c2d2025-08-20T03:26:25ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/806471806471Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture ExperimentsAli Erkoc0Esra Emiroglu1Kadri Ulas Akay2Department of Statistics, Faculty of Science and Letters, Mimar Sinan Fine Arts University, Sisli, 34380 Istanbul, TurkeyDepartment of Mathematics, Faculty of Science, Istanbul University, Beyazit, 34134 Istanbul, TurkeyDepartment of Mathematics, Faculty of Science, Istanbul University, Beyazit, 34134 Istanbul, TurkeyIn mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.http://dx.doi.org/10.1155/2014/806471
spellingShingle Ali Erkoc
Esra Emiroglu
Kadri Ulas Akay
Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
The Scientific World Journal
title Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
title_full Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
title_fullStr Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
title_full_unstemmed Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
title_short Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments
title_sort graphical evaluation of the ridge type robust regression estimators in mixture experiments
url http://dx.doi.org/10.1155/2014/806471
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AT esraemiroglu graphicalevaluationoftheridgetyperobustregressionestimatorsinmixtureexperiments
AT kadriulasakay graphicalevaluationoftheridgetyperobustregressionestimatorsinmixtureexperiments