An instrumental variable method for point processes: generalized Wald estimation based on deconvolution

• 成果类型: Article
• 署名作者: Jiang, Zhichao; Chen, Shizhe; Ding, Peng
• 署名单位: Sun Yat Sen University; University of California System; University of California Davis; University of California System; University of California Berkeley
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad005
• 发表日期: 2023
• 页码: 9891008
• 关键词: nonparametric deconvolution; Gaussian process; models; identification; SUBJECT

摘要

Point processes are probabilistic tools for modelling event data. While there exists a fast-growing literature on the relationships between point processes, how such relationships connect to causal effects remains unexplored. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome, and thus takes the form of deconvolution. We refer to this approach as generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods.