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On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference


  • Sebastian Calonico
  • Matias D. Cattaneo
  • Max H. Farrell


Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the mean-squared error (MSE)-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too “large.” Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available. Supplementary materials for this article are available online.

Suggested Citation

  • Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:767-779
    DOI: 10.1080/01621459.2017.1285776

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    References listed on IDEAS

    1. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    2. Kline, Patrick & Santos, Andres, 2012. "Higher order properties of the wild bootstrap under misspecification," Journal of Econometrics, Elsevier, vol. 171(1), pages 54-70.
    3. Berry S. M. & Carroll R. J & Ruppert D., 2002. "Bayesian Smoothing and Regression Splines for Measurement Error Problems," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 160-169, March.
    4. Alberto Abadie & Guido W. Imbens, 2008. "Estimation of the Conditional Variance in Paired Experiments," Annals of Economics and Statistics, GENES, issue 91-92, pages 175-187.
    5. Susanne M Schennach, 2020. "A Bias Bound Approach to Non-parametric Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(5), pages 2439-2472.
    6. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    8. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2013. "Generalized Jackknife Estimators of Weighted Average Derivatives," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1243-1256, December.
    9. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, June.
    10. repec:adr:anecst:y:2008:i:91-92:p:09 is not listed on IDEAS
    11. Song Xi Chen & Yong Song Qin, 2002. "Confidence Intervals Based on Local Linear Smoother," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 89-99, March.
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