{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T08:43:39Z","timestamp":1790930619847,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2002,5,16]],"date-time":"2002-05-16T00:00:00Z","timestamp":1021507200000},"content-version":"unspecified","delay-in-days":45,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2002,4]]},"abstract":"<jats:p>We consider an additive model with second-order interaction \nterms. Both marginal integration estimators and a combined \nbackfitting-integration estimator are proposed for all components \nof the model and their derivatives. The corresponding asymptotic \ndistributions are derived. Moreover, two test statistics for \ntesting the presence of interactions are proposed. Asymptotics \nfor the test functions and local power results are obtained. \nBecause direct implementation of the test procedure based on \nthe asymptotics would produce inaccurate results unless the \nnumber of observations is very large, a bootstrap procedure \nis provided, which is applicable for small or moderate sample \nsizes. Further, based on these methods a general test for \nadditivity is developed. Estimation and testing methods are \nshown to work well in simulation studies. Finally, our methods \nare illustrated on a five-dimensional production function for \na set of Wisconsin farm data. In particular, the separability \nhypothesis for the production function is discussed.<\/jats:p>","DOI":"10.1017\/s0266466602182016","type":"journal-article","created":{"date-parts":[[2002,11,14]],"date-time":"2002-11-14T17:01:57Z","timestamp":1037293317000},"page":"197-251","source":"Crossref","is-referenced-by-count":119,"title":["NONPARAMETRIC ESTIMATION AND TESTING OF INTERACTION IN ADDITIVE \nMODELS"],"prefix":"10.1017","volume":"18","author":[{"given":"Stefan","family":"Sperlich","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dag","family":"Tj\u00f8stheim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lijian","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2002,5,16]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602182016","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T16:33:03Z","timestamp":1554654783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602182016\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,4]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0266466602182016"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602182016","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,4]]}}}