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On the post selection inference constant under restricted isometry properties
- Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.
| Verfasserangaben: | Francois Bachoc, Gilles BlanchardGND, Pierre Neuvial |
|---|---|
| DOI: | https://doi.org/10.1214/18-EJS1490 |
| ISSN: | 1935-7524 |
| Titel des übergeordneten Werks (Englisch): | Electronic journal of statistics |
| Verlag: | Institute of Mathematical Statistics |
| Verlagsort: | Cleveland |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Datum der Erstveröffentlichung: | 20.11.2018 |
| Erscheinungsjahr: | 2018 |
| Datum der Freischaltung: | 24.02.2022 |
| Freies Schlagwort / Tag: | Inference post model-selection; PoSI constants; confidence intervals; high-dimensional inference; linear regression; restricted isometry property; sparsity |
| Band: | 12 |
| Ausgabe: | 2 |
| Seitenanzahl: | 22 |
| Erste Seite: | 3736 |
| Letzte Seite: | 3757 |
| Fördernde Institution: | german DFGGerman Research Foundation (DFG) [FOR-1735]; german DFG, under Collaborative Research Center [SFB-1294]; [ANR-16-CE40-0019] |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer Review: | Referiert |
| Publikationsweg: | Open Access / Gold Open-Access |
