A Bernstein-type inequality for suprema of random processes with an application to statistics
| dc.creator | Baraud, Yannick | |
| dc.date | 2009-04-21 | |
| dc.date.accessioned | 2026-07-07T13:06:54Z | |
| dc.date.available | 2026-07-07T13:06:54Z | |
| dc.description | We use the generic chaining device proposed by Talagrand to establish exponential bounds on the deviation probability of some suprema of random processes. Then, given a random vector $ξ$ in $\R^{n}$ the components of which are independent and admit a suitable exponential moment, we deduce a deviation inequality for the squared Euclidean norm of the projection of $ξ$ onto a linear subspace of $\R^{n}$. Finally, we provide an application of such an inequality to statistics, performing model selection in the regression setting when the errors are possibly non-Gaussian and the collection of models possibly large. | |
| dc.identifier | https://arxiv.org/abs/0904.3295 | |
| dc.identifier | http://arxiv.org/abs/0904.3295 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227928 | |
| dc.subject | Statistics Theory | |
| dc.subject | 60G70, 62G08 | |
| dc.title | A Bernstein-type inequality for suprema of random processes with an application to statistics | |
| dc.type | text |