{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T01:36:42Z","timestamp":1790991402901,"version":"4.1.0"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T00:00:00Z","timestamp":1674432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,11,15]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1093\/biomet\/asad005","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T14:50:51Z","timestamp":1674485451000},"page":"989-1008","source":"Crossref","is-referenced-by-count":6,"title":["An instrumental variable method for point processes: generalized Wald estimation based on deconvolution"],"prefix":"10.1093","volume":"110","author":[{"given":"Zhichao","family":"Jiang","sequence":"first","affiliation":[{"name":"Sun Yat-sen University School of Mathematics, , Guangzhou, Guangdong 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shizhe","family":"Chen","sequence":"additional","affiliation":[{"name":"University of California Department of Statistics, , Davis, One Shields Avenue, Davis, California 95616, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Ding","sequence":"additional","affiliation":[{"name":"University of California Department of Statistics, , Berkeley, 425 Evans Hall, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,1,23]]},"reference":[{"key":"2023112720115248200_B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4615-7397-5_1","article-title":"A model for nonparametric regression analysis of counting processes","volume-title":"Mathematical Statistics and Probability Theory","author":"Aalen,","year":"1980"},{"key":"2023112720115248200_B2","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","article-title":"Identification of causal effects using instrumental variables","volume":"91","author":"Angrist,","year":"1996","journal-title":"J. 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