Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models
Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estima...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2015-06-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/23231.pdf |
| _version_ | 1811302403602907136 |
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| author | S.K. Ghoreishi A. Mostafavinia |
| author_facet | S.K. Ghoreishi A. Mostafavinia |
| author_sort | S.K. Ghoreishi |
| collection | DOAJ |
| description | Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators have efficient asymptotic properties in spite of the fact they involve numerous hyperparameters. In this work, we propose a methodology for estimating the hyperparameters whenever one deals with multi-level heteroscedastic hierarchical normal model with several explanatory variables. we investigate the asymptotic properties of the shrinkage estimators when the shrinkage location hyperparameter lies within a suitable interval based on the sample range of the data. Moreover, we show our methodology performs much better in real data sets compared to available approaches. |
| first_indexed | 2024-04-13T07:27:28Z |
| format | Article |
| id | doaj.art-f7ec5043b14a4afa981bd3d526313a7b |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-13T07:27:28Z |
| publishDate | 2015-06-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-f7ec5043b14a4afa981bd3d526313a7b2022-12-22T02:56:26ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872015-06-0114210.2991/jsta.2015.14.2.8Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear modelsS.K. GhoreishiA. MostafaviniaEmpirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators have efficient asymptotic properties in spite of the fact they involve numerous hyperparameters. In this work, we propose a methodology for estimating the hyperparameters whenever one deals with multi-level heteroscedastic hierarchical normal model with several explanatory variables. we investigate the asymptotic properties of the shrinkage estimators when the shrinkage location hyperparameter lies within a suitable interval based on the sample range of the data. Moreover, we show our methodology performs much better in real data sets compared to available approaches.https://www.atlantis-press.com/article/23231.pdfAsymptotic optimality; Heteroscedasticity; Multiple linear regression; Shrinkage estimators; Stein’s unbiased risk estimate(SURE) |
| spellingShingle | S.K. Ghoreishi A. Mostafavinia Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models Journal of Statistical Theory and Applications (JSTA) Asymptotic optimality; Heteroscedasticity; Multiple linear regression; Shrinkage estimators; Stein’s unbiased risk estimate(SURE) |
| title | Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models |
| title_full | Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models |
| title_fullStr | Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models |
| title_full_unstemmed | Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models |
| title_short | Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models |
| title_sort | shrinkage estimates for multi level heteroscedastic hierarchical normal linear models |
| topic | Asymptotic optimality; Heteroscedasticity; Multiple linear regression; Shrinkage estimators; Stein’s unbiased risk estimate(SURE) |
| url | https://www.atlantis-press.com/article/23231.pdf |
| work_keys_str_mv | AT skghoreishi shrinkageestimatesformultilevelheteroscedastichierarchicalnormallinearmodels AT amostafavinia shrinkageestimatesformultilevelheteroscedastichierarchicalnormallinearmodels |