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For quadratic functional relationships with possibly non-normal errors, we present a consistent estimator when the error covariance matrix is known. A large sample test of the quadratic against the linear functional relationship is also suggested in this case.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1985.tb01381.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:35:11Z","timestamp":1544164511000},"page":"510-518","source":"Crossref","is-referenced-by-count":14,"title":["On the Polynomial Functional Relationship"],"prefix":"10.1093","volume":"47","author":[{"given":"Lai K.","family":"Chan","sequence":"first","affiliation":[{"name":"University of Manitoba \u00a0 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tak K.","family":"Mak","sequence":"additional","affiliation":[{"name":"University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921102680100_rssb01381-cit-0001","first-page":"29","article-title":"Estimating linear functional relationships","volume-title":"Recent Developments in Statistical Inference and Data Analysis.","author":"Chan","year":"1980"},{"key":"2024090921102680100_rssb01381-cit-0002","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1214\/aos\/1176345330","article-title":"Estimation in a multivariate \u201cerrors in variables\u201d regression model: large sample results","volume":"9","author":"Gleser","year":"1981","journal-title":"Ann. 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