Inference for location and height of peaks of a standardized field after selection
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915651928457216 |
|---|---|
| author | Green, Alden Taylor, Jonathan |
| author_facet | Green, Alden Taylor, Jonathan |
| contents | Peak inference concerns the use of local maxima ("peaks") of a noisy random field to detect and localize regions where underlying signal is present. We propose a peak inference method that first subjects observed peaks to a significance test of the null hypothesis that no signal is present, and then uses the peaks that are declared significant to construct post-selectively valid confidence regions for the location and height of nearby true peaks. We analyze the performance of this method in a smooth signal plus constant variance noise model under a high-curvature asymptotic assumption, and prove that it asymptotically controls both the number of false discoveries, and the number of confidence regions that do not contain a true peak, relative to the number of points at which inference is conducted. An important intermediate theoretical result uses the Kac-Rice formula to derive a novel approximation to the intensity function of a point process that counts local maxima, which is second-order accurate under the alternative, nearby high-curvature true peaks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inference for location and height of peaks of a standardized field after selection Green, Alden Taylor, Jonathan Methodology Statistics Theory Peak inference concerns the use of local maxima ("peaks") of a noisy random field to detect and localize regions where underlying signal is present. We propose a peak inference method that first subjects observed peaks to a significance test of the null hypothesis that no signal is present, and then uses the peaks that are declared significant to construct post-selectively valid confidence regions for the location and height of nearby true peaks. We analyze the performance of this method in a smooth signal plus constant variance noise model under a high-curvature asymptotic assumption, and prove that it asymptotically controls both the number of false discoveries, and the number of confidence regions that do not contain a true peak, relative to the number of points at which inference is conducted. An important intermediate theoretical result uses the Kac-Rice formula to derive a novel approximation to the intensity function of a point process that counts local maxima, which is second-order accurate under the alternative, nearby high-curvature true peaks. |
| title | Inference for location and height of peaks of a standardized field after selection |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2512.04059 |