Smooth predictive model fitting in regression.
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| Title: | Smooth predictive model fitting in regression. |
|---|---|
| Authors: | Burman, Prabir1 pburman@ucdavis.edu, Paul, Debashis1 debpaul@ucdavis.edu |
| Source: | Journal of Multivariate Analysis. Mar2017, Vol. 155, p165-179. 15p. |
| Subjects: | Statistical smoothing, Prediction models, Regression analysis, Stochastic convergence, Gaussian processes |
| Abstract: | We propose a smooth hypothesis-testing type method for model fitting in regression and develop its theoretical properties in a moderately high-dimensional setting. We derive the asymptotic behavior of the L 2 prediction risk and the optimal choice of the threshold-determining parameter under the Gaussian regression framework with orthogonal covariates. When the covariates are not orthogonal, this method can be used in conjunction with some reasonable procedures for orthogonalizing the covariates, such as a stepwise regression coupled with the Gram–Schmidt procedure. Simulation results show that our proposed method often outperforms its competitors. Asymptotic approximation of the mean square error of the proposed estimator is obtained and it is shown that the optimal rate of convergence depends on the behavior of the smoothing function at zero. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 121260066 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Smooth predictive model fitting in regression. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burman%2C+Prabir%22">Burman, Prabir</searchLink><relatesTo>1</relatesTo><i> pburman@ucdavis.edu</i><br /><searchLink fieldCode="AR" term="%22Paul%2C+Debashis%22">Paul, Debashis</searchLink><relatesTo>1</relatesTo><i> debpaul@ucdavis.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Multivariate+Analysis%22">Journal of Multivariate Analysis</searchLink>. Mar2017, Vol. 155, p165-179. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Statistical+smoothing%22">Statistical smoothing</searchLink><br /><searchLink fieldCode="DE" term="%22Prediction+models%22">Prediction models</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+analysis%22">Regression analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We propose a smooth hypothesis-testing type method for model fitting in regression and develop its theoretical properties in a moderately high-dimensional setting. We derive the asymptotic behavior of the L 2 prediction risk and the optimal choice of the threshold-determining parameter under the Gaussian regression framework with orthogonal covariates. When the covariates are not orthogonal, this method can be used in conjunction with some reasonable procedures for orthogonalizing the covariates, such as a stepwise regression coupled with the Gram–Schmidt procedure. Simulation results show that our proposed method often outperforms its competitors. Asymptotic approximation of the mean square error of the proposed estimator is obtained and it is shown that the optimal rate of convergence depends on the behavior of the smoothing function at zero. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=121260066 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jmva.2016.12.010 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 165 Subjects: – SubjectFull: Statistical smoothing Type: general – SubjectFull: Prediction models Type: general – SubjectFull: Regression analysis Type: general – SubjectFull: Stochastic convergence Type: general – SubjectFull: Gaussian processes Type: general Titles: – TitleFull: Smooth predictive model fitting in regression. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burman, Prabir – PersonEntity: Name: NameFull: Paul, Debashis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 0047259X Numbering: – Type: volume Value: 155 Titles: – TitleFull: Journal of Multivariate Analysis Type: main |
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