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Orthogonal Series Estimation of Nonparametric Regression Measurement Error Models with Validation Data
College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
- 1 College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
Applied Mathematics·Volume 08 (2017)·Pages 1820–1831·Published 4 December 2017·DOI10.4236/am.2017.812130
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Abstract
In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption. The convergence rates of the proposed estimator are derived. By example and through simulation, the method is robust against the misspecification of a measurement error model.
KeywordsIll-Posed Inverse ProblemsMeasurement ErrorsNonparametric RegressionOrthogonal SeriesValidation Data
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