A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem
KAUST Grant NumberKUS-CI-016-04
Permanent link to this recordhttp://hdl.handle.net/10754/597252
MetadataShow full item record
AbstractLocal 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.
CitationDelaigle 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.
SponsorsCarroll'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.
PublisherInforma UK Limited
PubMed Central IDPMC2846380
CollectionsPublications Acknowledging KAUST Support
- Local Polynomial Regression for Symmetric Positive Definite Matrices.
- Authors: Yuan Y, Zhu H, Lin W, Marron JS
- Issue date: 2012 Sep 1
- Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes.
- Authors: Li D, Li R
- Issue date: 2016 Sep
- Density estimation in the presence of heteroscedastic measurement error of unknown type using phase function deconvolution.
- Authors: Nghiem L, Potgieter CJ
- Issue date: 2018 Nov 10
- Local CQR Smoothing: An Efficient and Safe Alternative to Local Polynomial Regression.
- Authors: Kai B, Li R, Zou H
- Issue date: 2010 Jan
- Continuously differentiable sample-spacing entropy estimation.
- Authors: Ozertem U, Uysal I, Erdogmus D
- Issue date: 2008 Nov