{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:48Z","timestamp":1760149788898,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971457","12201601","2208085"],"award-info":[{"award-number":["11971457","12201601","2208085"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Anhui Provincial Natural Science Foundation","award":["11971457","12201601","2208085"],"award-info":[{"award-number":["11971457","12201601","2208085"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the L1 criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data.<\/jats:p>","DOI":"10.3390\/e25091327","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:34:12Z","timestamp":1694554452000},"page":"1327","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Detection of Interaction Effects in a Nonparametric Concurrent Regression Model"],"prefix":"10.3390","volume":"25","author":[{"given":"Rui","family":"Pan","sequence":"first","affiliation":[{"name":"School of Data Science, University of Science and Technology of China, Hefei 230026, China"}]},{"given":"Zhanfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei 230026, China"}]},{"given":"Yaohua","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei 230026, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1111\/rssb.12257","article-title":"Detecting and dating structural breaks in functional data without dimension reduction","volume":"80","author":"Aue","year":"2018","journal-title":"J. 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