Robust Bayesian Regularized Estimation Based on t Regression Model
The t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable se...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2015/989412 |
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| _version_ | 1832546181190778880 |
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| author | Zean Li Weihua Zhao |
| author_facet | Zean Li Weihua Zhao |
| author_sort | Zean Li |
| collection | DOAJ |
| description | The t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso t regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the t distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian t regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers. |
| format | Article |
| id | doaj-art-21a228f8742243fd8cd57c7a7d6c66f0 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-21a228f8742243fd8cd57c7a7d6c66f02025-02-03T07:23:35ZengWileyJournal of Probability and Statistics1687-952X1687-95382015-01-01201510.1155/2015/989412989412Robust Bayesian Regularized Estimation Based on t Regression ModelZean Li0Weihua Zhao1School of Computer Science and Technology, Nantong University, Nantong 226019, ChinaSchool of Science, Nantong University, Nantong 226019, ChinaThe t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso t regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the t distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian t regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.http://dx.doi.org/10.1155/2015/989412 |
| spellingShingle | Zean Li Weihua Zhao Robust Bayesian Regularized Estimation Based on t Regression Model Journal of Probability and Statistics |
| title | Robust Bayesian Regularized Estimation Based on t Regression Model |
| title_full | Robust Bayesian Regularized Estimation Based on t Regression Model |
| title_fullStr | Robust Bayesian Regularized Estimation Based on t Regression Model |
| title_full_unstemmed | Robust Bayesian Regularized Estimation Based on t Regression Model |
| title_short | Robust Bayesian Regularized Estimation Based on t Regression Model |
| title_sort | robust bayesian regularized estimation based on t regression model |
| url | http://dx.doi.org/10.1155/2015/989412 |
| work_keys_str_mv | AT zeanli robustbayesianregularizedestimationbasedontregressionmodel AT weihuazhao robustbayesianregularizedestimationbasedontregressionmodel |