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Simple and Honest Confidence Intervals in Nonparametric Regression

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Abstract

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean-squared error results in CIs that are nearly efficient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n^{-2/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in a Monte Carlo analysis and an empirical application.

Suggested Citation

  • Timothy B. Armstrong & Michal Koles�r, 2016. "Simple and Honest Confidence Intervals in Nonparametric Regression," Cowles Foundation Discussion Papers 2044R3, Cowles Foundation for Research in Economics, Yale University, revised Aug 2018.
  • Handle: RePEc:cwl:cwldpp:2044r3
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    1. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
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    3. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 79-99, March.
    4. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    5. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 933-959.
    6. Alberto Abadie & Guido W. Imbens & Fanyin Zheng, 2014. "Inference for Misspecified Models With Fixed Regressors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1601-1614, December.
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    More about this item

    Keywords

    Nonparametric inference; relative efficiency;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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