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

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

Abstract

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

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    1. Susanne M. Schennach, 2015. "A bias bound approach to nonparametric inference," CeMMAP working papers CWP71/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. 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.
    3. 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.
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    Cited by:

    1. De Benedetto, Marco Alberto, 2018. "Quality of Politicians and Electoral System. Evidence from a Quasi-experimental Design for Italian Cities," MPRA Paper 89511, University Library of Munich, Germany.
    2. Niklas Potrafke & Felix Roesel, 2019. "The urban-rural gap in health care infrastructure - does government ideology matter?," CESifo Working Paper Series 7647, CESifo Group Munich.
    3. Pietro Bonaldi & Mauricio Villamizar-Villegas, 2018. "An Auction-Based Test of Private Information in an Interdealer FX Market," Borradores de Economia 1049, Banco de la Republica de Colombia.
    4. Marlon Fritz, 2019. "Data-Driven Local Polynomial Trend Estimation for Economic Data - Steady State Adjusting Trends," Working Papers Dissertations 49, Paderborn University, Faculty of Business Administration and Economics.
    5. Cattaneo, Matias D. & Crump, Richard K. & Farrell, Max H. & Schaumburg, Ernst, 2016. "Characteristic-sorted portfolios: estimation and inference," Staff Reports 788, Federal Reserve Bank of New York, revised 01 Feb 2019.
    6. Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2018. "Simple Local Polynomial Density Estimators," Papers 1811.11512, arXiv.org, revised Jun 2019.
    7. repec:eee:anture:v:74:y:2019:i:c:p:1-16 is not listed on IDEAS
    8. Yuanhua Feng & Thomas Gries, 2017. "Data-driven local polynomial for the trend and its derivatives in economic time series," Working Papers CIE 102, Paderborn University, CIE Center for International Economics.
    9. repec:kap:pubcho:v:177:y:2018:i:1:d:10.1007_s11127-018-0591-8 is not listed on IDEAS
    10. Delis, Manthos & Fringuellotti, Fulvia & Ongena, Steven, 2019. "Credit and Income," CEPR Discussion Papers 13468, C.E.P.R. Discussion Papers.
    11. repec:tpr:restat:v:101:y:2019:i:2:p:264-278 is not listed on IDEAS
    12. repec:eee:econom:v:207:y:2018:i:1:p:129-161 is not listed on IDEAS
    13. Marco Alberto De Benedetto, 2018. "Quality of Politicians and Electoral System. Evidence from a Quasi-experimental Design for Italian Cities," BCAM Working Papers 1802, Birkbeck Centre for Applied Macroeconomics.
    14. Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Yingjie Feng, 2019. "Binscatter Regressions," Papers 1902.09615, arXiv.org.
    15. Pellegrini, Guido & Tarola, Ornella & Cerqua, Augusto & Ceccantoni, Giulia, 2018. "Can regional policies shape migration flows?," MPRA Paper 87874, University Library of Munich, Germany.

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