On Deconvolution as a First Stage Nonparametric Estimator
We reconsider Taupin’s (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to the class of range-restricted distributions, then weak smoothness assumptions suffice to ensure sqrt(n) consistency of the estimator. The restriction to such distributions is innocuous, because it does not affect the fit to the data. Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.
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- Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 145-168.
- Newey, Whitney K, 1994.
"The Asymptotic Variance of Semiparametric Estimators,"
Econometric Society, vol. 62(6), pages 1349-1382, November.
- Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
- Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
- Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
- Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
- Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
- Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366. Full references (including those not matched with items on IDEAS)
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