A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem
Type
ArticleKAUST Grant Number
KUS-CI-016-04Date
2009-03Permanent link to this record
http://hdl.handle.net/10754/597252
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Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.Citation
Delaigle A, Fan J, Carroll RJ (2009) A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem. Journal of the American Statistical Association 104: 348–359. Available: http://dx.doi.org/10.1198/jasa.2009.0114.Sponsors
Carroll's research was supported by grants from the National Cancer Institute (CA57030, CA90301) and by award number KUS-CI-016-04 made by the King Abdullah University of Science and Technology (KAUST). Delaigle's research was supported by a Maurice Belz Fellowship from the University of Melbourne, Australia, and by a grant from the Australian Research Council. Fan's research was supported by grants from the National Institute of General Medicine R01-GM072611 and National Science Foundation DMS-0714554 and DMS-0751568. The authors thank the editor, the associate editor, and referees for their valuable comments.Publisher
Informa UK LimitedPubMed ID
20351800PubMed Central ID
PMC2846380ae974a485f413a2113503eed53cd6c53
10.1198/jasa.2009.0114
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