Open Access
February 2001 Semi-Parametric Estimation in the Nonlinear Structural Errors-in-Variables Model
Marie-Luce Taupin
Ann. Statist. 29(1): 66-93 (February 2001). DOI: 10.1214/aos/996986502


In the nonlinear structural errors-in-variables model, we propose a consistent estimator of the unknown parameter using a modified least squares criterion. We give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n-1/2. Nevertheless, the rate is of order n-1/2 for some particular analytic regression functions. For instance, when the regression function is either a polynomial function or an exponential function, we prove that our estimator achieves the parametric rate of convergence.


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Marie-Luce Taupin. "Semi-Parametric Estimation in the Nonlinear Structural Errors-in-Variables Model." Ann. Statist. 29 (1) 66 - 93, February 2001.


Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62039
MathSciNet: MR1833959
Digital Object Identifier: 10.1214/aos/996986502

Primary: 62F12 , 62J02
Secondary: 62G05 , 62G20

Keywords: Analytic function , Errors-in-variables model , Fourier transform , nonparametric estimation , semi-parametric estimation

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 1 • February 2001
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