Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 3, Issue 5) |
| DOI | 10.11648/j.ajtas.20140305.15 |
| Page(s) | 148-166 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
AIC, BIC, AICc, HQC, Kullback-Leibler (K-L) Distance, Model Averaging, Model Selection
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APA Style
Magda Mohamed Mohamed Haggag. (2014). New Criteria of Model Selection and Model Averaging in Linear Regression Models. American Journal of Theoretical and Applied Statistics, 3(5), 148-166. https://doi.org/10.11648/j.ajtas.20140305.15
ACS Style
Magda Mohamed Mohamed Haggag. New Criteria of Model Selection and Model Averaging in Linear Regression Models. Am. J. Theor. Appl. Stat. 2014, 3(5), 148-166. doi: 10.11648/j.ajtas.20140305.15
AMA Style
Magda Mohamed Mohamed Haggag. New Criteria of Model Selection and Model Averaging in Linear Regression Models. Am J Theor Appl Stat. 2014;3(5):148-166. doi: 10.11648/j.ajtas.20140305.15
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Download@article{10.11648/j.ajtas.20140305.15,
author = {Magda Mohamed Mohamed Haggag},
title = {New Criteria of Model Selection and Model Averaging in Linear Regression Models},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {3},
number = {5},
pages = {148-166},
doi = {10.11648/j.ajtas.20140305.15},
url = {https://doi.org/10.11648/j.ajtas.20140305.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140305.15},
abstract = {Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.},
year = {2014}
}
TY - JOUR T1 - New Criteria of Model Selection and Model Averaging in Linear Regression Models AU - Magda Mohamed Mohamed Haggag Y1 - 2014/10/20 PY - 2014 N1 - https://doi.org/10.11648/j.ajtas.20140305.15 DO - 10.11648/j.ajtas.20140305.15 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 148 EP - 166 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20140305.15 AB - Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection. VL - 3 IS - 5 ER -
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