Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles"
| dc.creator | Chamandy, N. | |
| dc.creator | Worsley, K. J. | |
| dc.creator | Taylor, J. | |
| dc.creator | Gosselin, F. | |
| dc.date | 2008-11-05 | |
| dc.date.accessioned | 2026-07-07T10:15:43Z | |
| dc.date.available | 2026-07-07T10:15:43Z | |
| dc.description | Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above $u$, denoted $\mathbb{E}φ(A_u)$. Under isotropy, one can use the expansion $\mathbb{E}φ(A_u)=\sum_k\mathcal{V}_kρ_k(u)$, where $\mathcal{V}_k$ is an intrinsic volume of the parameter space and $ρ_k$ is an EC density of the field. EC densities are available for a number of processes, mainly those constructed from (multivariate) Gaussian fields via smooth functions. Using saddlepoint methods, we derive an expansion for $ρ_k(u)$ for fields which are only approximately Gaussian, but for which higher-order cumulants are available. We focus on linear combinations of $n$ independent non-Gaussian fields, whence a Central Limit theorem is in force. The threshold $u$ is allowed to grow with the sample size $n$, in which case our expression has a smaller relative asymptotic error than the Gaussian EC density. Several illustrative examples including an application to "bubbles" data accompany the theory. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AOS549 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0811.0757 | |
| dc.identifier | http://arxiv.org/abs/0811.0757 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 5, 2471-2507 | |
| dc.identifier | doi:10.1214/07-AOS549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173266 | |
| dc.subject | Statistics Theory | |
| dc.subject | 60G60, 62E20, 62M40 (Primary) 53A99, 58E05, 60B12, 60F05 (Secondary) | |
| dc.title | Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles" | |
| dc.type | text |