{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:16:27Z","timestamp":1782288987114,"version":"3.54.5"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T00:00:00Z","timestamp":1696377600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T00:00:00Z","timestamp":1696377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation","award":["SES-1853209"],"award-info":[{"award-number":["SES-1853209"]}]},{"name":"National Science Foundation","award":["SES-1853209"],"award-info":[{"award-number":["SES-1853209"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s11222-023-10299-z","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T15:01:31Z","timestamp":1696431691000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Modern non-linear function-on-function regression"],"prefix":"10.1007","volume":"33","author":[{"given":"Aniruddha Rajendra","family":"Rao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthew","family":"Reimherr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"issue":"499","key":"10299_CR1","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1080\/01621459.2012.716337","volume":"107","author":"TT Cai","year":"2012","unstructured":"Cai, T.T., Yuan, M.: Minimax and adaptive prediction for functional linear regression. J. Am. Stat. Assoc. 107(499), 1201\u20131216 (2012)","journal-title":"J. Am. Stat. Assoc."},{"key":"10299_CR2","first-page":"11","volume":"39","author":"D Chen","year":"2012","unstructured":"Chen, D., Hall, P., M\u00fcller, H.: Single and multiple index functional regression models with nonparametric link. Ann. Stat. 39, 11 (2012)","journal-title":"Ann. Stat."},{"key":"10299_CR3","doi-asserted-by":"crossref","unstructured":"Conan-Guez, B., Rossi, F.: Multi-layer perceptrons for functional data analysis: a projection based approach. In: ICANN (2002)","DOI":"10.1007\/3-540-46084-5_109"},{"issue":"2","key":"10299_CR4","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.chemolab.2009.02.001","volume":"96","author":"PH Eilers","year":"2009","unstructured":"Eilers, P.H., Li, B., Marx, B.D.: Multivariate calibration with single-index signal regression. Chemom. Intell. Lab. Syst. 96(2), 196\u2013202 (2009)","journal-title":"Chemom. Intell. Lab. Syst."},{"issue":"5","key":"10299_CR5","doi-asserted-by":"publisher","first-page":"2296","DOI":"10.1214\/15-AOS1346","volume":"43","author":"Y Fan","year":"2015","unstructured":"Fan, Y., James, G.M., Radchenko, P.: Functional additive regression. Ann. Stat. 43(5), 2296\u20132325 (2015)","journal-title":"Ann. Stat."},{"key":"10299_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13748-012-0035-5","volume":"2","author":"H Fanaee-T","year":"2013","unstructured":"Fanaee-T, H., Gama, J.: Event labeling combining ensemble detectors and background knowledge. Prog. Artif. Intell. 2, 1\u201315 (2013)","journal-title":"Prog. Artif. Intell."},{"key":"10299_CR7","doi-asserted-by":"crossref","unstructured":"Ferraty, F.: Recent advances in functional data analysis and related topics (2011)","DOI":"10.1007\/978-3-7908-2736-1"},{"key":"10299_CR8","series-title":"Springer Series in Statistics","volume-title":"Nonparametric Functional Data Analysis: Theory and Practice","author":"F Ferraty","year":"2006","unstructured":"Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics, Springer, Berlin (2006)"},{"key":"10299_CR9","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s11749-012-0306-2","volume":"22","author":"F Ferraty","year":"2013","unstructured":"Ferraty, F., Goia, A., Salinelli, E., Vieu, P.: Functional projection pursuit regression. TEST 22, 293\u2013320 (2013)","journal-title":"TEST"},{"key":"10299_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-3655-3","volume-title":"Inference for Functional Data with Applications","author":"L Horv\u00e1th","year":"2012","unstructured":"Horv\u00e1th, L., Kokoszka, P.: Inference for Functional Data with Applications. Springer, New York (2012)"},{"key":"10299_CR11","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1198\/016214504000001556","volume":"100","author":"G James","year":"2004","unstructured":"James, G., Silverman, B.: Functional adaptive model estimation. J. Am. Stat. Assoc. 100, 565\u2013576 (2004)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10299_CR12","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1214\/10-AOS845","volume":"39","author":"C-R Jiang","year":"2011","unstructured":"Jiang, C.-R., Wang, J.-L.: Functional single index models for longitudinal data. Ann. Stat. 39(1), 362\u2013388 (2011)","journal-title":"Ann. Stat."},{"key":"10299_CR13","unstructured":"Kadri, H., Duflos, E., Preux, P., Canu, S., Davy, M.: Nonlinear functional regression: a functional RKHS approach. In: Teh, Y.W., Titterington, M. (eds.) Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, vol. 9, pp. 374\u2013380. Chia Laguna Resort, Sardinia (2010)"},{"key":"10299_CR14","unstructured":"Kang, H.B., Reimherr, M., Shriver, M., Claes, P.: Manifold data analysis with applications to high-frequency 3D imaging (2017)"},{"issue":"1","key":"10299_CR15","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1080\/10618600.2017.1356730","volume":"27","author":"JS Kim","year":"2018","unstructured":"Kim, J.S., Staicu, A.-M., Maity, A., Carroll, R.J., Ruppert, D.: Additive function-on-function regression. J. Comput. Graph. Stat. 27(1), 234\u2013244 (2018)","journal-title":"J. Comput. Graph. Stat."},{"key":"10299_CR16","volume-title":"Introduction to Functional Data Analysis","author":"P Kokoszka","year":"2018","unstructured":"Kokoszka, P., Reimherr, M.: Introduction to Functional Data Analysis. CRC, New York (2018)"},{"issue":"4","key":"10299_CR17","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1002\/cjs.5550350410","volume":"35","author":"H Lian","year":"2007","unstructured":"Lian, H.: Nonlinear functional models for functional responses in reproducing kernel Hilbert spaces. Can. J. Stat. 35(4), 597\u2013606 (2007)","journal-title":"Can. J. Stat."},{"key":"10299_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jmva.2016.05.003","volume":"150","author":"H Ma","year":"2016","unstructured":"Ma, H., Zhu, Z.: Continuously dynamic additive models for functional data. J. Multivar. Anal. 150, 1\u201313 (2016)","journal-title":"J. Multivar. Anal."},{"issue":"8","key":"10299_CR19","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1002\/env.905","volume":"19","author":"L Magnano","year":"2008","unstructured":"Magnano, L., Boland, J.W., Hyndman, R.J.: Generation of synthetic sequences of half-hourly temperature. Environmetrics 19(8), 818\u2013835 (2008)","journal-title":"Environmetrics"},{"issue":"1","key":"10299_CR20","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1080\/10618600.2012.729985","volume":"23","author":"MW McLean","year":"2014","unstructured":"McLean, M.W., Hooker, G., Staicu, A., Scheipl, F., Ruppert, D.: Functional generalized additive models. J. Comput. Graph. Stat. 23(1), 249\u2013269 (2014)","journal-title":"J. Comput. Graph. Stat."},{"key":"10299_CR21","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1146\/annurev-statistics-010814-020413","volume":"2","author":"J Morris","year":"2014","unstructured":"Morris, J.: Functional regression. Annu. Rev. Stat. Appl. 2, 321\u2013359 (2014)","journal-title":"Annu. Rev. Stat. Appl."},{"key":"10299_CR22","doi-asserted-by":"publisher","first-page":"1534","DOI":"10.1198\/016214508000000751","volume":"103","author":"H Muller","year":"2008","unstructured":"Muller, H., Yao, F.: Functional additive models. J. Am. Stat. Assoc. 103, 1534\u20131544 (2008)","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"10299_CR23","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1093\/biomet\/ast004","volume":"100","author":"H Muller","year":"2013","unstructured":"Muller, H., Wu, Y., Yao, F.: Continuously additive models for nonlinear functional regression. Biometrika 100(3), 607\u2013622 (2013)","journal-title":"Biometrika"},{"key":"10299_CR24","unstructured":"Olver, P.J.: Introduction to the calculus of variations (2019)"},{"issue":"3","key":"10299_CR25","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1016\/j.jspi.2006.06.011","volume":"137","author":"C Preda","year":"2007","unstructured":"Preda, C.: Regression models for functional data by reproducing kernel Hilbert spaces methods. J. Stat. Plan. Inference 137(3), 829\u2013840 (2007). https:\/\/doi.org\/10.1016\/j.jspi.2006.06.011. (Special Issue on Nonparametric Statistics and Related Topics: In honor of M.L. Puri)","journal-title":"J. Stat. Plan. Inference"},{"key":"10299_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-7107-7","volume-title":"Functional Data Analysis","author":"J Ramsay","year":"1997","unstructured":"Ramsay, J., Silverman, B.: Functional Data Analysis. Springer, Berlin (1997)"},{"key":"10299_CR27","unstructured":"Rao, A.R., Reimherr, M.: Non-linear functional modeling using neural networks (2021)"},{"key":"10299_CR28","doi-asserted-by":"crossref","unstructured":"Reimherr, M., Sriperumbudur, B., Taoufik, B.: Optimal prediction for additive function-on-function regression (2017)","DOI":"10.1214\/18-EJS1505"},{"key":"10299_CR29","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1111\/insr.12163","volume":"85","author":"P Reiss","year":"2016","unstructured":"Reiss, P., Goldsmith, J., Shang, H.L., Ogden, R.: Methods for scalar-on-function regression. Int. Stat. Rev. 85, 228\u2013249 (2016)","journal-title":"Int. Stat. Rev."},{"key":"10299_CR30","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s11063-005-3100-2","volume":"23","author":"F Rossi","year":"2006","unstructured":"Rossi, F., Conan-Guez, B.: Theoretical properties of projection based multilayer perceptrons with functional inputs. Neural Process. Lett. 23, 55\u201370 (2006)","journal-title":"Neural Process. Lett."},{"key":"10299_CR31","doi-asserted-by":"crossref","unstructured":"Rossi, F., Conan-Guez, B., Fleuret, F.: Functional data analysis with multi layer perceptrons. In: Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN\u201902 (cat. no.02ch37290), vol.\u00a03, pp.\u00a02843\u20132848 (2002)","DOI":"10.1109\/IJCNN.2002.1007599"},{"issue":"2","key":"10299_CR32","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1080\/10618600.2014.901914","volume":"24","author":"F Scheipl","year":"2015","unstructured":"Scheipl, F., Staicu, A.-M., Greven, S.: Functional additive mixed models. J. Comput. Graph. Stat. 24(2), 477\u2013501 (2015)","journal-title":"J. Comput. Graph. Stat."},{"issue":"6","key":"10299_CR33","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.2307\/1914309","volume":"54","author":"TM Stoker","year":"1986","unstructured":"Stoker, T.M.: Consistent estimation of scaled coefficients. Econometrica 54(6), 1461\u20131481 (1986)","journal-title":"Econometrica"},{"issue":"524","key":"10299_CR34","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1080\/01621459.2017.1356320","volume":"113","author":"X Sun","year":"2018","unstructured":"Sun, X., Du, P., Wang, X., Ma, P.: Optimal penalized function-on-function regression under a reproducing kernel Hilbert space framework. J. Am. Stat. Assoc. 113(524), 1601\u20131611 (2018)","journal-title":"J. Am. Stat. Assoc."},{"key":"10299_CR35","doi-asserted-by":"publisher","first-page":"106814","DOI":"10.1016\/j.csda.2019.106814","volume":"142","author":"Y Sun","year":"2020","unstructured":"Sun, Y., Wang, Q.: Function-on-function quadratic regression models. Comput. Stat. Data Anal. 142, 106814 (2020)","journal-title":"Comput. Stat. Data Anal."},{"key":"10299_CR36","first-page":"567","volume":"2","author":"X Wang","year":"2013","unstructured":"Wang, X., Ruppert, D.: Optimal prediction in an additive functional model. Stat. Sin. 2, 567\u2013589 (2013)","journal-title":"Stat. Sin."},{"key":"10299_CR38","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zheng, S., Farahat, A., Serita, S., Saeki, T., Gupta, C.: Multilayer perceptron for sparse functional data. In: 2019 International joint conference on neural networks (IJCNN), pp.\u00a01\u201310 (2019b)","DOI":"10.1109\/IJCNN.2019.8851700"},{"key":"10299_CR39","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zheng, S., Farahat, A., Serita, S., Saeki, T., Gupta, C.: Multilayer perceptron for sparse functional data. In: 2019 International joint conference on neural networks (IJCNN), pp.\u00a01\u201310 (2019)","DOI":"10.1109\/IJCNN.2019.8851700"},{"key":"10299_CR37","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zheng, S., Farahat, A., Serita, S., Gupta, C.: Remaining useful life estimation using functional data analysis (2019a)","DOI":"10.1109\/ICPHM.2019.8819420"},{"issue":"1","key":"10299_CR40","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1093\/biomet\/asp069","volume":"97","author":"F Yao","year":"2010","unstructured":"Yao, F., Muller, H.: Functional quadratic regression. Biometrika 97(1), 49\u201364 (2010)","journal-title":"Biometrika"},{"key":"10299_CR41","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1111\/rssb.12036","volume":"76","author":"H Zhu","year":"2013","unstructured":"Zhu, H., Yao, F., Zhang, H.: Structured functional additive regression in reproducing kernel Hilbert spaces. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 76, 581\u2013603 (2013)","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10299-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-023-10299-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10299-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:56:17Z","timestamp":1730249777000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-023-10299-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,4]]},"references-count":41,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["10299"],"URL":"https:\/\/doi.org\/10.1007\/s11222-023-10299-z","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,4]]},"assertion":[{"value":"27 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"130"}}