Relaxing the Gaussian assumption in shrinkage and SURE in high dimension
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics
2022
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| _version_ | 1797108003174875136 |
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| author | Fathi, M Goldstein, L Reinert, G Saumard, A |
| author_facet | Fathi, M Goldstein, L Reinert, G Saumard, A |
| author_sort | Fathi, M |
| collection | OXFORD |
| description | Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein’s Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the Gaussian through the use of tools developed in the probabilistic area now known as Stein’s method. We show that shrinkage is efficient away from the Gaussian under very mild conditions on the distribution of the noise. SURE is also proved to be adaptive under similar assumptions, and in particular in a way that retains the classical asymptotics of Pinsker’s theorem. Notably, shrinkage and SURE are shown to be efficient under mild distributional assumptions, and particularly for general isotropic log-concave measures. |
| first_indexed | 2024-03-07T07:23:25Z |
| format | Journal article |
| id | oxford-uuid:c9ab5f82-daf7-4d86-9b02-1dd0f638d3a5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:23:25Z |
| publishDate | 2022 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:c9ab5f82-daf7-4d86-9b02-1dd0f638d3a52022-10-31T11:41:50ZRelaxing the Gaussian assumption in shrinkage and SURE in high dimensionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c9ab5f82-daf7-4d86-9b02-1dd0f638d3a5EnglishSymplectic ElementsInstitute of Mathematical Statistics2022Fathi, MGoldstein, LReinert, GSaumard, AShrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein’s Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the Gaussian through the use of tools developed in the probabilistic area now known as Stein’s method. We show that shrinkage is efficient away from the Gaussian under very mild conditions on the distribution of the noise. SURE is also proved to be adaptive under similar assumptions, and in particular in a way that retains the classical asymptotics of Pinsker’s theorem. Notably, shrinkage and SURE are shown to be efficient under mild distributional assumptions, and particularly for general isotropic log-concave measures. |
| spellingShingle | Fathi, M Goldstein, L Reinert, G Saumard, A Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title | Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title_full | Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title_fullStr | Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title_full_unstemmed | Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title_short | Relaxing the Gaussian assumption in shrinkage and SURE in high dimension |
| title_sort | relaxing the gaussian assumption in shrinkage and sure in high dimension |
| work_keys_str_mv | AT fathim relaxingthegaussianassumptioninshrinkageandsureinhighdimension AT goldsteinl relaxingthegaussianassumptioninshrinkageandsureinhighdimension AT reinertg relaxingthegaussianassumptioninshrinkageandsureinhighdimension AT saumarda relaxingthegaussianassumptioninshrinkageandsureinhighdimension |