Entropy Estimate For High Dimensional Monotonic Functions
| dc.creator | Gao, Fuchang | |
| dc.creator | Wellner, Jon A. | |
| dc.date | 2005-12-29 | |
| dc.date.accessioned | 2026-07-07T08:07:26Z | |
| dc.date.available | 2026-07-07T08:07:26Z | |
| dc.description | We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for $p<d/(d-1)$ and $p>d/(d-1)$. We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a $d$-dimensional monotone density. | |
| dc.description | 11 pages. Submitted to Journal of Multivariate Analysis. See also http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.html | |
| dc.identifier | https://arxiv.org/abs/math/0512641 | |
| dc.identifier | http://arxiv.org/abs/math/0512641 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130941 | |
| dc.subject | Statistics Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 41A46, 46E35 (primary), 62G05, 62G07 (secondary) | |
| dc.title | Entropy Estimate For High Dimensional Monotonic Functions | |
| dc.type | text |