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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| 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. |
| format | Article |
| id | doaj-art-5bd00af060e54e45be20e7e3129b8c2d |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| 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 |
| work_keys_str_mv | AT alierkoc graphicalevaluationoftheridgetyperobustregressionestimatorsinmixtureexperiments AT esraemiroglu graphicalevaluationoftheridgetyperobustregressionestimatorsinmixtureexperiments AT kadriulasakay graphicalevaluationoftheridgetyperobustregressionestimatorsinmixtureexperiments |