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Regressions with Berkson errors in covariates - A nonparametric approach

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  • Susanne M. Schennach

Abstract

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.

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  • Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
  • Handle: RePEc:arx:papers:1308.2836
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    1. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
    2. 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.
    3. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    4. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    5. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    6. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    7. 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.
    8. 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, March.
    9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    10. 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.
    11. 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.
    12. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    13. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
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    Cited by:

    1. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    2. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. repec:eee:econom:v:200:y:2017:i:2:p:154-168 is not listed on IDEAS
    4. Sriya Iyer & Chander Velu & Melvyn Weeks, 2014. "Divine Competition: Religious Organisations and Service Provision in India," Cambridge Working Papers in Economics 1409, Faculty of Economics, University of Cambridge.
    5. repec:bla:biomet:v:72:y:2016:i:4:p:1369-1377 is not listed on IDEAS

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