TY - JOUR
T1 - A design-adaptive local polynomial estimator for the errors-in-variables problem
AU - Delaigle, Aurore
AU - Fan, Jianqing
AU - Fan, Raymond J.Carroll
N1 - Funding Information:
Aurore Delaigle is Reader, Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK and Department of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia (E-mail: [email protected]). Jianqing Fan is Frederick L. Moore’18 Professor of Finance, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, and Honored Professor, Department of Statistics, Shanghai University of Finance and Economics, Shanghai, China (E-mail: [email protected]). Raymond J. Carroll is Distinguished Professor, Department of Statistics, Texas A&M University, College Station, TX 77843 (E-mail: [email protected]). 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.
PY - 2009/3
Y1 - 2009/3
N2 - 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.
AB - 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.
KW - Bandwidth selector
KW - Deconvolution
KW - Inverse problems
KW - Local polynomial
KW - Measurement errors
KW - Nonparametric regression
KW - Replicated measurements
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U2 - 10.1198/jasa.2009.0114
DO - 10.1198/jasa.2009.0114
M3 - Article
C2 - 20351800
AN - SCOPUS:70349761934
SN - 0162-1459
VL - 104
SP - 348
EP - 359
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 485
ER -