{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T05:06:56Z","timestamp":1739423216422,"version":"3.37.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"ISM Cooperative Research Program","award":["2024-ISMCRP-4404"],"award-info":[{"award-number":["2024-ISMCRP-4404"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Inf. Secur."],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s10207-024-00973-2","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T16:56:38Z","timestamp":1736268998000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Theoretical lower bounds for one-dimensional locally private estimations with missing data"],"prefix":"10.1007","volume":"24","author":[{"given":"Hajime","family":"Ono","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"973_CR1","doi-asserted-by":"publisher","unstructured":"Duchi, J.C., Jordan, M.I., Wainwright, M.J.: Local Privacy and Statistical Minimax Rates. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science. 429\u2013438 (2013). https:\/\/doi.org\/10.1109\/FOCS.2013.53","DOI":"10.1109\/FOCS.2013.53"},{"issue":"3","key":"973_CR2","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1137\/090756090","volume":"40","author":"SP Kasiviswanathan","year":"2011","unstructured":"Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? SIAM J. Comput. 40(3), 793\u2013826 (2011). https:\/\/doi.org\/10.1137\/090756090","journal-title":"SIAM J. Comput."},{"key":"973_CR3","doi-asserted-by":"publisher","unstructured":"Erlingsson, \u00da., Pihur, V., Korolova, A.: RAPPOR: Randomized aggregatable privacy-preserving ordinal response. In: Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security. 1054\u20131067 (2014). https:\/\/doi.org\/10.1145\/2660267.2660348","DOI":"10.1145\/2660267.2660348"},{"key":"973_CR4","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1515\/popets-2016-0015","volume":"3","author":"G Fanti","year":"2016","unstructured":"Fanti, G., Pihur, V., Erlingsson, \u00da.: Building a RAPPOR with the unknown: privacy-preserving learning of associations and data dictionaries. Proc. Priv. Enhanc. Technol. 3, 41\u201361 (2016). https:\/\/doi.org\/10.1515\/popets-2016-0015","journal-title":"Proc. Priv. Enhanc. Technol."},{"key":"973_CR5","doi-asserted-by":"publisher","unstructured":"Bassily, R., Smith, A.: Local, private, efficient protocols for succinct histograms. In Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing. 127\u2013135 (2015). https:\/\/doi.org\/10.1145\/2746539.2746632","DOI":"10.1145\/2746539.2746632"},{"key":"973_CR6","doi-asserted-by":"publisher","unstructured":"Qin, Z., Yang, Y., Yu, T., Khalil, I., Xiao, X., Ren, K.: Heavy hitter estimation over set-valued data with local differential privacy. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security. 192\u2013203 (2016). https:\/\/doi.org\/10.1145\/2976749.2978409","DOI":"10.1145\/2976749.2978409"},{"key":"973_CR7","unstructured":"Kairouz, P., Bonawitz, K., Ramage, D.: Discrete distribution estimation under local privacy. In: Proceedings of The 33rd International Conference on Machine Learning. 48, 2436\u20132444 (2016). https:\/\/proceedings.mlr.press\/v48\/kairouz16.html"},{"key":"973_CR8","unstructured":"Ding, B., Kulkarni, J., Yekhanin, S.: Collecting telemetry data privately. In: Advances in Neural Information Processing Systems 30 (NIPS 2017). 3574-3583 (2017). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2017\/hash\/253614bbac999b38b5b60cae531c4969-Abstract.html"},{"key":"973_CR9","doi-asserted-by":"publisher","unstructured":"Ding, B., Nori, H., Li, P., Allen, J.: Comparing population means under local differential privacy: with significance and power. In: Thirty-Second AAAI Conference on Artificial Intelligence. 32(1), 26\u201333 (2018). https:\/\/doi.org\/10.1609\/aaai.v32i1.11301","DOI":"10.1609\/aaai.v32i1.11301"},{"key":"973_CR10","unstructured":"Gaboardi, M., Rogers, R.: Local private hypothesis testing: chi-square tests. In: Proceedings of the 35th International Conference on Machine Learning. 1626\u20131635 (2018). https:\/\/proceedings.mlr.press\/v80\/gaboardi18a.html"},{"key":"973_CR11","unstructured":"Wang, D. Xu, J.: On sparse linear regression in the local differential privacy model. In: Proceedings of the 36th International Conference on Machine Learning. 6628\u20136637 (2019). https:\/\/proceedings.mlr.press\/v97\/wang19m.html"},{"issue":"24","key":"973_CR12","doi-asserted-by":"publisher","first-page":"7030","DOI":"10.3390\/s20247030","volume":"20","author":"T Wang","year":"2020","unstructured":"Wang, T., Zhang, X., Feng, J., Yang, X.: A comprehensive survey on local differential privacy toward data statistics and analysis. Sensors 20(24), 7030 (2020). https:\/\/doi.org\/10.3390\/s20247030","journal-title":"Sensors"},{"key":"973_CR13","unstructured":"Apple Differential Privacy Team: Learning with privacy at scale. https:\/\/machinelearning.apple.com\/2017\/12\/06\/learning-with-privacy-at-scale.html (2017). Accessed 7 March 2023"},{"issue":"521","key":"973_CR14","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1080\/01621459.2017.1389735","volume":"113","author":"JC Duchi","year":"2018","unstructured":"Duchi, J.C., Jordan, M.I., Wainwright, M.J.: Minimax optimal procedures for locally private estimation. J. Am. Stat. Assoc. 113(521), 182\u2013201 (2018). https:\/\/doi.org\/10.1080\/01621459.2017.1389735","journal-title":"J. Am. Stat. Assoc."},{"key":"973_CR15","unstructured":"Duchi, J.C., Rogers, R.: Lower bounds for locally private estimation via communication complexity. In: Proceedings of Machine Learning Research. 99, 1161\u20131191 (2019). https:\/\/proceedings.mlr.press\/v99\/duchi19a.html"},{"key":"973_CR16","unstructured":"Kairouz, P., Oh, S., Viswanath, P.: Extremal mechanisms for local differential privacy. In: Advances in Neural Information Processing Systems. 27 (2014). https:\/\/proceedings.neurips.cc\/paper\/2014\/file\/86df7dcfd896fcaf2674f757a2463eba-Paper.pdf"},{"issue":"8","key":"973_CR17","doi-asserted-by":"publisher","first-page":"5662","DOI":"10.1109\/TIT.2018.2809790","volume":"64","author":"M Ye","year":"2018","unstructured":"Ye, M., Barg, A.: Optimal schemes for discrete distribution estimation under locally differential privacy. IEEE Trans. Inf. Theory. 64(8), 5662\u20135676 (2018). https:\/\/doi.org\/10.1109\/TIT.2018.2809790","journal-title":"IEEE Trans. Inf. Theory."},{"key":"973_CR18","unstructured":"Carpenter, J., Kenward, M.: Guidelines for handling missing data in Social Science Research. https:\/\/www.lshtm.ac.uk\/media\/37311 (2005). Accessed 8 February 2022"},{"key":"973_CR19","unstructured":"Eurostat: Practical Guide to Data Validation in Eurostat (2007 Edition). https:\/\/ec.europa.eu\/eurostat\/ramon\/nomenclatures\/index.cfm?TargetUrl=DSP_NOM_DTL_VIEW&StrNom=STATMANUAL &StrLanguageCode=EN &IntPcKey=50606238 &IntKey=50606270 &StrLayoutCode=HIERARCHIC &IntCurrentPage=1 (2007). Accessed 26 March 2023"},{"key":"973_CR20","unstructured":"United Nations. Economic Commission for Africa: manual for statistical development indicators. https:\/\/repository.uneca.org\/handle\/10855\/43074 (2019). Accessed 26 March 2023"},{"key":"973_CR21","doi-asserted-by":"publisher","DOI":"10.1002\/9781119482260","volume-title":"Statistical Analysis with Missing Data","author":"RJA Little","year":"2019","unstructured":"Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data, 3rd edn. John Wiley & Sons, Hoboken (2019). https:\/\/doi.org\/10.1002\/9781119482260","edition":"3"},{"key":"973_CR22","doi-asserted-by":"publisher","unstructured":"Loh, P., Wainwright, M. J.: Corrupted and missing predictors: minimax bounds for high-dimensional linear regression. In: 2012 IEEE International Symposium on Information Theory Proceedings. 2601\u20132605 (2012). https:\/\/doi.org\/10.1109\/ISIT.2012.6283989","DOI":"10.1109\/ISIT.2012.6283989"},{"issue":"4","key":"973_CR23","first-page":"591","volume":"24","author":"N Bates","year":"2008","unstructured":"Bates, N., Dahlhamer, J., Singer, E.: Privacy concerns, too busy, or just not interested: using doorstep concerns to predict survey nonresponse. J. Off. Stat. 24(4), 591\u2013612 (2008)","journal-title":"J. Off. Stat."},{"key":"973_CR24","unstructured":"Ekin, E.: New Poll: 62% Say the Political Climate Prevents Them from Sharing Political Views. https:\/\/www.cato.org\/blog\/new-poll-62-say-political-climate-prevents-them-sharing-political-views (2020). Accessed 8 February 2022"},{"key":"973_CR25","doi-asserted-by":"publisher","unstructured":"Sun, H., Dong, B., Wang, H., T., Yu, T., Qin, Z.: Truth inference on sparse crowdsourcing data with local differential privacy. In: 2018 IEEE International Conference on Big Data (Big Data). 488\u2013497 (2018). https:\/\/doi.org\/10.1109\/BigData.2018.8622635","DOI":"10.1109\/BigData.2018.8622635"},{"key":"973_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-59410-7_6","author":"L Sun","year":"2020","unstructured":"Sun, L., Ye, X., Zhao, J., Lu, C., Yang, M.: BiSample: bidirectional sampling for handling missing data with local differential privacy. Database Syst. Adv. Appl. (2020). https:\/\/doi.org\/10.1007\/978-3-030-59410-7_6","journal-title":"Database Syst. Adv. Appl."},{"key":"973_CR27","doi-asserted-by":"publisher","unstructured":"Ye, Q., Hu, H., Li, N., Meng, X., Zheng, H., Yan, H.: Beyond value perturbation: local differential privacy in the temporal setting. In: IEEE INFOCOM 2021 - IEEE Conference on Computer Communications. 1\u201310 (2021).https:\/\/doi.org\/10.1109\/INFOCOM42981.2021.9488899","DOI":"10.1109\/INFOCOM42981.2021.9488899"},{"key":"973_CR28","volume-title":"Introduction to Nonparametric Estimation","author":"AB Tsybakov","year":"2008","unstructured":"Tsybakov, A.B.: Introduction to Nonparametric Estimation. Springer Science & Business Media, Cham (2008)"},{"key":"973_CR29","doi-asserted-by":"publisher","unstructured":"Joseph, M., Mao, J., Neel, S., Roth, A.: The role of interactivity in local differential privacy. In: 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS). 94\u2013105 (2019). https:\/\/doi.org\/10.1109\/FOCS.2019.00015","DOI":"10.1109\/FOCS.2019.00015"},{"key":"973_CR30","doi-asserted-by":"publisher","unstructured":"Smith, A., Thakurta, A., Upadhyay, J.: Is interaction necessary for distributed private learning? In: 2017 IEEE Symposium on Security and Privacy (SP). 58\u201377 (2017). https:\/\/doi.org\/10.1109\/SP.2017.35","DOI":"10.1109\/SP.2017.35"},{"key":"973_CR31","volume-title":"Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis","author":"M Mitzenmacher","year":"2017","unstructured":"Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis. Cambridge University Press, Cambridge (2017)"},{"key":"973_CR32","doi-asserted-by":"publisher","unstructured":"Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Foundations and Trends\u00ae in Theoretical Computer Science. 9, 3\u20134, 211\u2013407 (2014). https:\/\/doi.org\/10.1561\/0400000042","DOI":"10.1561\/0400000042"},{"key":"973_CR33","doi-asserted-by":"publisher","unstructured":"Raginsky, M.: Strong data processing inequalities and $$\\Phi $$-Sobolev inequalities for discrete channels. IEEE Trans. Inf. Theory 62(6), 3355\u20133389 (2016). https:\/\/doi.org\/10.1109\/TIT.2016.2549542","DOI":"10.1109\/TIT.2016.2549542"},{"key":"973_CR34","unstructured":"Portal Site of Official Statistics of Japan website: Number of private households by Size of household - Japan, Prefectures, Municipalities. https:\/\/www.e-stat.go.jp\/en\/dbview?sid=0003445278 (2021). Accessed 30 October 2024"},{"key":"973_CR35","doi-asserted-by":"crossref","unstructured":"Pereira, R.C., Abreu, P.H., Rodrigues, P.P., Figueiredo, M.A.T.: Imputation of data Missing Not at Random: artificial generation and benchmark analysis. Expert Syst. Appl. 249, 123654 (2024). (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0957417424005207)","DOI":"10.1016\/j.eswa.2024.123654"}],"container-title":["International Journal of Information Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10207-024-00973-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10207-024-00973-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10207-024-00973-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T05:19:09Z","timestamp":1739337549000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10207-024-00973-2"}},"subtitle":["Proofs with three types of missing mechanisms"],"short-title":[],"issued":{"date-parts":[[2025,1,7]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["973"],"URL":"https:\/\/doi.org\/10.1007\/s10207-024-00973-2","relation":{},"ISSN":["1615-5262","1615-5270"],"issn-type":[{"type":"print","value":"1615-5262"},{"type":"electronic","value":"1615-5270"}],"subject":[],"published":{"date-parts":[[2025,1,7]]},"assertion":[{"value":"7 January 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author has not received an honorarium from any company.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article contains no studies with human participants.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The code of simulation performed in Sect.\u00a0 is contained in the supplemental material.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Material and\/or code availability"}}],"article-number":"58"}}