{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multiresolution-analysis-of-point-processes","title":"Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation","arxiv_id":"1803.11202","date":"2018-03-29","proceeding":null,"authors":["Youssef Taleb","Edward A. K. Cohen"],"abstract":"We take a wavelet based approach to the analysis of point processes and the estimation of the first order intensity under a continuous time setting. A multiresolution analysis of a point process is formulated which motivates the definition of homogeneity at different scales of resolution, termed $J$-th level homogeneity. Further to this, the activity in a point processes' first order behavior at different scales of resolution is also defined and termed $L$-th level innovation. Likelihood ratio tests for both these properties are proposed with asymptotic distributions provided, even when only a single realization of the point process is observed. The test for $L$-th level innovation forms the basis for a collection of statistical strategies for thresholding coefficients in a wavelet based estimator of the intensity function. These thresholding strategies are shown to outperform the existing local hard thresholding strategy on a range of simulation scenarios.","url_abs":"http://arxiv.org/abs/1803.11202v1","url_pdf":"http://arxiv.org/pdf/1803.11202v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"multiresolution-analysis-of-point-processes","repo_url":"https://github.com/YoussefT/Statistical-thresholding","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}