Sebastian Calonico, Matias D. Cattaneo, Max H. Farrell
arXiv 12 Aug 2015 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2017) · 346 citations (OpenAlex)
arXiv:1508.02973 · PDF · DOI · OpenAlex · Extracted main text
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 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | height .65ex depth -.6ex width 3em\ (1992) b), Effect of Bias Estimation on Coverage Accuracy of Bootstrap Confidence Intervals for a Probability Density | 1.000 | 14 | 7 | 100% |
| 2 | Hall, P., and Horowitz, J. L (2013) A Simple Bootstrap Method for Constructing Nonparametric Confidence Bands for Functions | 1.000 | 13 | 6 | 100% |
| 3 | height .65ex depth -.6ex width 3em\ (1992) a) | 1.000 | 8 | 3 | 100% |
| 4 | Fan, J., and Gijbels, I (1996) Local polynomial modelling and its applications | 1.000 | 7 | 5 | 100% |
| 5 | height .65ex depth -.6ex width 3em\ (2017) nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference | 1.000 | 6 | 5 | 100% |
| 6 | Gasser, T., Muller, H.-G., and Mammitzsch, V (1985) Kernels for Nonparametric Curve Estimation | 1.000 | 6 | 3 | 100% |
| 7 | Chen, S. X., and Qin, Y. S (2002) Confidence Intervals Based on Local Linear Smoother | 0.928 | 4 | 3 | 100% |
| 8 | Loader, C (2013) locfit: Local Regression, Likelihood and Density Estimation | 0.928 | 4 | 3 | 100% |
| 9 | Schucany, W., and Sommers, J. P (1977) Improvement of Kernel Type Density Estimators | 0.874 | 5 | 2 | 100% |
| 10 | Singh, R. S (1977) Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density | 0.811 | 4 | 2 | 100% |
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