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Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non-parametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase-transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data-generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts.<\/jats:p>","DOI":"10.1111\/rssb.12554","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T12:36:11Z","timestamp":1667392571000},"page":"1851-1885","source":"Crossref","is-referenced-by-count":18,"title":["Linear Regression and Its Inference on Noisy Network-Linked Data"],"prefix":"10.1093","volume":"84","author":[{"given":"Can M.","family":"Le","sequence":"first","affiliation":[{"name":"Department of Statistics , , Davis , California , USA"},{"name":"University of California, Davis , , Davis , California , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianxi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistics , , Charlottesville , Virginia , USA"},{"name":"University of Virginia , , Charlottesville , Virginia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"2023030906294912300_","first-page":"1","article-title":"Community detection and stochastic block models: recent developments","volume":"18","author":"Abbe","year":"2018","journal-title":"Journal of Machine Learning Research"},{"key":"2023030906294912300_","volume-title":"Entrywise eigenvector analysis of random matrices with low expected rank. arXiv preprint arXiv:1709.09565","author":"Abbe","year":"2017"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1179\/0024363914Z.00000000087","article-title":"The impact of family structure on the health of children: effects of divorce","volume":"81","author":"Anderson","year":"2014","journal-title":"The Linacre Quarterly"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1177\/0081175018782569","article-title":"Limitations of design-based causal inference and a\/b testing under arbitrary and network interference","volume":"48","author":"Basse","year":"2018","journal-title":"Sociological Methodology"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1093\/biomet\/asy036","article-title":"Model-assisted design of experiments in the presence of network-correlated outcomes","volume":"105","author":"Basse","year":"2018","journal-title":"Biometrika"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","article-title":"Laplacian eigenmaps for dimensionality reduction and data representation","volume":"15","author":"Belkin","year":"2003","journal-title":"Neural Computation"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-7618-4","volume-title":"Applied spatial data analysis with R","author":"Bivand","year":"2013","edition":"2nd edition"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/rsa.20168","article-title":"The phase transition in inhomogeneous random graphs","volume":"31","author":"Bollobas","year":"2007","journal-title":"Random Structures and Algorithms"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.jeconom.2008.12.021","article-title":"Identification of peer effects through social networks","volume":"150","author":"Bramoull\u00e9","year":"2009","journal-title":"Journal of Econometrics"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0378-8733(02)00038-2","article-title":"Network inference, error, and informant (in) accuracy: a Bayesian approach","volume":"25","author":"Butts","year":"2003","journal-title":"Social Networks"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","article-title":"Exact matrix completion via convex optimization","volume":"9","author":"Cand\u00e8s","year":"2009","journal-title":"Foundations of Computational Mathematics"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The power of convex relaxation: near-optimal matrix completion","volume":"56","author":"Cand\u00e8s","year":"2010","journal-title":"IEEE Transactions on Information Theory"},{"key":"2023030906294912300_","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1214\/18-AOS1752","article-title":"The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics","volume":"47","author":"Cape","year":"2019","journal-title":"The Annals of Statistics"},{"key":"2023030906294912300_","volume-title":"Econometrics of sampled networks. 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