Altieri L, Farcomeni A, Fegatelli DA. Continuous time-interaction processes for population size estimation, with an application to drug dealing in Italy.
Biometrics 2022. [PMID:
35289395 DOI:
10.1111/biom.13662]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 03/07/2022] [Indexed: 11/30/2022]
Abstract
We introduce a time-interaction point process where the occurrence of an event can increase (self-excitement) or reduce (self-correction) the probability of future events. Self-excitement and self-correction are allowed to be triggered by the same event, at different time scales; other effects such as those of covariates, unobserved heterogeneity, and temporal dependence are also allowed in the model. We focus on capture-recapture data, as our work is motivated by an original example about estimation of the total number of drug dealers in Italy. To do so, we derive a conditional likelihood formulation where only subjects with at least one capture are involved in the inference process. The result is a novel and flexible continuous-time population size estimator. A simulation study and the analysis of our motivating example illustrate the validity of our approach in several scenarios. This article is protected by copyright. All rights reserved.
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