Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables
Model selection uncertainty has drawn a lot of attention from academics recently because it significantly affects parameter estimation and prediction. Scholars are currently addressing and quantifying uncertainty in model selection by concentrating on model combining and model confidence sets. In th...
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| Format: | Article |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/664 |
| _version_ | 1797264175042396160 |
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| author | Faguang Wen Jiming Jiang Yihui Luan |
| author_facet | Faguang Wen Jiming Jiang Yihui Luan |
| author_sort | Faguang Wen |
| collection | DOAJ |
| description | Model selection uncertainty has drawn a lot of attention from academics recently because it significantly affects parameter estimation and prediction. Scholars are currently addressing and quantifying uncertainty in model selection by concentrating on model combining and model confidence sets. In this paper, we present a new approach for building model confidence sets, which we call AMac. We provide a theoretical lower bound on the degree of confidence in the model confidence sets that AMac has built. Furthermore, we discuss how the implementation of current model confidence set construction methods becomes difficult when dealing with high-dimensional variables. To address this problem, we suggest building model selection paths (MSP) as a solution. We develop an algorithm for building MSP and show its effectiveness by utilizing the theories of adaptive lasso and lars. We perform an extensive set of simulation experiments to compare the performances of Mac and AMac methods. According to the results, AMac is more stable when there are fluctuations in noise levels. The model confidence sets built by AMac, in particular, achieve coverage rates that are closer to the desired confidence level, especially in the presence of high noise levels. To further confirm that MSP can successfully generate model confidence sets that maintain the given confidence level as the sample size increases, we conduct extensive simulation tests with high-dimensional variables. Ultimately, we hope that the strategies and concepts discussed in this work will improve results in subsequent research on the uncertainty of model selection. |
| first_indexed | 2024-04-25T00:24:43Z |
| format | Article |
| id | doaj.art-b086a1e71bcd4315a4c24077b42d8fef |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:24:43Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b086a1e71bcd4315a4c24077b42d8fef2024-03-12T16:49:52ZengMDPI AGMathematics2227-73902024-02-0112566410.3390/math12050664Model Selection Path and Construction of Model Confidence Set under High-Dimensional VariablesFaguang Wen0Jiming Jiang1Yihui Luan2Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, ChinaDepartment of Statistics, University of California, Davis, CA 95616, USAFrontiers Science Center for Nonlinear Expectations (Ministry of Education), Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, ChinaModel selection uncertainty has drawn a lot of attention from academics recently because it significantly affects parameter estimation and prediction. Scholars are currently addressing and quantifying uncertainty in model selection by concentrating on model combining and model confidence sets. In this paper, we present a new approach for building model confidence sets, which we call AMac. We provide a theoretical lower bound on the degree of confidence in the model confidence sets that AMac has built. Furthermore, we discuss how the implementation of current model confidence set construction methods becomes difficult when dealing with high-dimensional variables. To address this problem, we suggest building model selection paths (MSP) as a solution. We develop an algorithm for building MSP and show its effectiveness by utilizing the theories of adaptive lasso and lars. We perform an extensive set of simulation experiments to compare the performances of Mac and AMac methods. According to the results, AMac is more stable when there are fluctuations in noise levels. The model confidence sets built by AMac, in particular, achieve coverage rates that are closer to the desired confidence level, especially in the presence of high noise levels. To further confirm that MSP can successfully generate model confidence sets that maintain the given confidence level as the sample size increases, we conduct extensive simulation tests with high-dimensional variables. Ultimately, we hope that the strategies and concepts discussed in this work will improve results in subsequent research on the uncertainty of model selection.https://www.mdpi.com/2227-7390/12/5/664model confidence setsmodel selectionvariable selectionhigh-dimensional variablesmodel averaginguncertainty in model selection |
| spellingShingle | Faguang Wen Jiming Jiang Yihui Luan Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables Mathematics model confidence sets model selection variable selection high-dimensional variables model averaging uncertainty in model selection |
| title | Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables |
| title_full | Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables |
| title_fullStr | Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables |
| title_full_unstemmed | Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables |
| title_short | Model Selection Path and Construction of Model Confidence Set under High-Dimensional Variables |
| title_sort | model selection path and construction of model confidence set under high dimensional variables |
| topic | model confidence sets model selection variable selection high-dimensional variables model averaging uncertainty in model selection |
| url | https://www.mdpi.com/2227-7390/12/5/664 |
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