Product Depth for Temporal Point Processes Observed Only Up to the First k Events
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914169399279616 |
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| author | Shen, Chifeng Fu, Yuejiao Shi, Xiaoping Chen, Michael |
| author_facet | Shen, Chifeng Fu, Yuejiao Shi, Xiaoping Chen, Michael |
| contents | Temporal point processes (TPPs) model the timing of discrete events along a timeline and are widely used in fields such as neuroscience and fi- nance. Statistical depth functions are powerful tools for analyzing centrality and ranking in multivariate and functional data, yet existing depth notions for TPPs remain limited. In this paper, we propose a novel product depth specifically designed for TPPs observed only up to the first k events. Our depth function comprises two key components: a normalized marginal depth, which captures the temporal distribution of the final event, and a conditional depth, which characterizes the joint distribution of the preceding events. We establish its key theoretical properties and demonstrate its practical utility through simulation studies and real data applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Product Depth for Temporal Point Processes Observed Only Up to the First k Events Shen, Chifeng Fu, Yuejiao Shi, Xiaoping Chen, Michael Methodology Statistics Theory 62G35 Temporal point processes (TPPs) model the timing of discrete events along a timeline and are widely used in fields such as neuroscience and fi- nance. Statistical depth functions are powerful tools for analyzing centrality and ranking in multivariate and functional data, yet existing depth notions for TPPs remain limited. In this paper, we propose a novel product depth specifically designed for TPPs observed only up to the first k events. Our depth function comprises two key components: a normalized marginal depth, which captures the temporal distribution of the final event, and a conditional depth, which characterizes the joint distribution of the preceding events. We establish its key theoretical properties and demonstrate its practical utility through simulation studies and real data applications. |
| title | Product Depth for Temporal Point Processes Observed Only Up to the First k Events |
| topic | Methodology Statistics Theory 62G35 |
| url | https://arxiv.org/abs/2511.19375 |