Regressions with Berkson errors in covariates - A nonparametric approach
This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These examples illustrate that Berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy.
|Date of creation:||Aug 2013|
|Date of revision:|
|Publication status:||Published in Annals of Statistics 2013, Vol. 41, No. 3, 1642-1668|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Susanne M. Schennach, 2004.
"Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models,"
Econometric Society 2004 North American Summer Meetings
602, Econometric Society.
- Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
- Aurore Delaigle & Peter Hall & Peihua Qiu, 2006. "Nonparametric methods for solving the Berkson errors-in-variables problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 201-220.
- D’Haultfoeuille, Xavier, 2011.
"On The Completeness Condition In Nonparametric Instrumental Problems,"
Cambridge University Press, vol. 27(03), pages 460-471, June.
- Xavier d'Haultfoeuille, 2006. "On the Completeness Condition in Nonparametric Instrumental Problems," Working Papers 2006-32, Centre de Recherche en Economie et Statistique.
- Bani Mallick & F. Owen Hoffman & Raymond J. Carroll, 2002. "Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site," Biometrics, The International Biometric Society, vol. 58(1), pages 13-20, 03.
- Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
- Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
- van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
- Raymond J. Carroll & Aurore Delaigle & Peter Hall, 2007. "Non-parametric regression estimation from data contaminated by a mixture of Berkson and classical errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 859-878.
- Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
- Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, 05.
- 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.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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