Simple and honest confidence intervals in nonparametric regression
By T. Armstrong, Michael J. Kolesar. Quantitative Economics, 2016
104 citations recorded by the source corpus.
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 use 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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d6c6de2f4cb7933c8b04dde54c0240618bac0874
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In Statistics and Probability
Citations in the corpus
- Inference in Regression Discontinuity Designs with a Discrete Running Variable (2016, unknown): “Proof of Proposition 1 We first derive the expression for rsup, following the arguments in Theorem B.1 in Armstrong and Kolesár (2016).”
- Regression Discontinuity Designs (2021, unknown): “Imbens and Wager (2019) and Armstrong and Kolesar (2020) apply ideas from Backus (1989) and Donoho (1994) to develop RD inference methods that are uniformly valid over a smoothness class of functions determining the largest possible misspecification bias of the RD treatment effect estimator.”
- Minimizing Sensitivity to Model Misspecification (2018, background): “Using a small- approximation is crucial for analytic tractability, since the variance term in (9) only needs to be calculated under the reference model, and the optimization problem (11) is convex.”
- External Validity in Fuzzy Regression Discontinuity Designs (2019, unknown): “…by HTV. Recent theoretical contributions include Porter (2003), McCrary (2008), Imbens and Kalyanaraman (2012), Calonico, Cattaneo, and Titiunik (2014, 2015), Dong and Lewbel (2015), Dong (2018), Bertanha (2017), Gelman and Imbens (2014), Armstrong and Kolesar (2018), and Imbens and Wager (2018).”