On weakly bounded empirical processes
| dc.creator | Mendelson, Shahar | |
| dc.date | 2005-12-23 | |
| dc.date.accessioned | 2026-07-07T06:55:44Z | |
| dc.date.available | 2026-07-07T06:55:44Z | |
| dc.description | Let $F$ be a class of functions on a probability space $(Ω,μ)$ and let $X_1,...,X_k$ be independent random variables distributed according to $μ$. We establish high probability tail estimates of the form $\sup_{f \in F} |\{i : |f(X_i)| \geq t \}$ using a natural parameter associated with $F$. We use this result to analyze weakly bounded empirical processes indexed by $F$ and processes of the form $Z_f=|k^{-1}\sum_{i=1}^k |f|^p(X_i)-\E|f|^p|$ for $p>1$. We also present some geometric applications of this approach, based on properties of the random operator $Γ=k^{-1/2}\sum_{i=1}^k \inr{X_i,\cdot}e_i$, where the $(X_i)_{i=1}^k$ are sampled according to an isotropic, log-concave measure on $\R^n$. | |
| dc.identifier | https://arxiv.org/abs/math/0512554 | |
| dc.identifier | http://arxiv.org/abs/math/0512554 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106378 | |
| dc.subject | Probability | |
| dc.title | On weakly bounded empirical processes | |
| dc.type | text |