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In contrast to existing approaches, the new formulation separates well the joint effects of covariates that cannot be accounted for by individual main effects. The new approach enables correct interpretation of interaction effects by making them orthogonal to the associated main effects in the $ L^{2} $ sense. A new method is developed to estimate the resulting main and interaction effects. Asymptotic $ L^{2} $ error rates are derived for the estimators under mild technical conditions. Numerical evidence is provided via simulation studies and real-data examples.<\/jats:p>","DOI":"10.1093\/biomet\/asaf074","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T11:35:45Z","timestamp":1761046545000},"source":"Crossref","is-referenced-by-count":1,"title":["Identification and estimation of interaction effects in nonparametric additive regression"],"prefix":"10.1093","volume":"113","author":[{"given":"Seung Hyun","family":"Moon","sequence":"first","affiliation":[{"name":"Department of Statistics, Seoul National University , 1 Gwanak-ro, Gwanak-gu , Seoul, \u00a0 msh94kr@snu.ac.kr","place":["South Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Byeong U","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Statistics, Seoul National University , 1 Gwanak-ro, Gwanak-gu , Seoul, \u00a0 bupark@snu.ac.kr","place":["South Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enno","family":"Mammen","sequence":"additional","affiliation":[{"name":"Institute for Mathematics, Heidelberg University , Im Neuenheimer Feld 205 , 69120 Heidelberg, \u00a0 mammen@math.uni-heidelberg.de","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young Kyung","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Information Statistics, Kangwon National University , 1 Kangwondaehak-gil, Chuncheon-si , Gangwon-do,","place":["South Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"2026032607090426200_asaf074-B1","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0012-365X(93)90410-U","article-title":"Two-way ANOVA models with unbalanced data","volume":"116","author":"Fujikoshi","year":"1993","journal-title":"Discrete Math"},{"key":"2026032607090426200_asaf074-B2","doi-asserted-by":"crossref","first-page":"2216","DOI":"10.1214\/17-AOS1617","article-title":"Smooth backfitting for errors-in-variables additive models","volume":"46","author":"Han","year":"2018","journal-title":"Ann. 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