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Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We also observe a phase transition phenomenon related to the interplay between the manifold dimension and the contamination level. We demonstrate via simulated and real data examples that the proposed method has favourable numerical performance relative to existing commonly used methods.<\/jats:p>","DOI":"10.1093\/biomet\/asaa041","type":"journal-article","created":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T21:53:23Z","timestamp":1589493203000},"page":"167-181","source":"Crossref","is-referenced-by-count":19,"title":["Functional regression on the manifold with contamination"],"prefix":"10.1093","volume":"108","author":[{"given":"Zhenhua","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Statistics and Applied Probability, National University of Singapore, 117546 Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Probability and Statistics, School of Mathematical Sciences, Center for Statistical Science, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,7,21]]},"reference":[{"key":"2021030708334357900_B1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1214\/10-AOS823","article-title":"Regression on manifolds: Estimation of the exterior derivative","volume":"39","author":"Aswani,","year":"2011","journal-title":"Ann. 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