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    A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem

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    Type
    Article
    Authors
    Delaigle, Aurore
    Fan, Jianqing
    Carroll, Raymond J.
    KAUST Grant Number
    KUS-CI-016-04
    Date
    2009-03
    Permanent link to this record
    http://hdl.handle.net/10754/597252
    
    Metadata
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    Abstract
    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 Limited
    Journal
    Journal of the American Statistical Association
    DOI
    10.1198/jasa.2009.0114
    PubMed ID
    20351800
    PubMed Central ID
    PMC2846380
    ae974a485f413a2113503eed53cd6c53
    10.1198/jasa.2009.0114
    Scopus Count
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