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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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File URL: http://arxiv.org/pdf/1308.2836
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1308.2836.

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Date of creation: Aug 2013
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Publication status: Published in Annals of Statistics 2013, Vol. 41, No. 3, 1642-1668
Handle: RePEc:arx:papers:1308.2836

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Web page: http://arxiv.org/

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  1. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, 05.
  2. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  3. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  4. 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.
  5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  6. 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.
  7. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  8. 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.
  9. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  10. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  11. 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.
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Cited by:
  1. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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