Simple and Honest Confidence Intervals in Nonparametric Regression

Timothy Armstrong and Michal Koles�r
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Michal Koles�r: Princeton University

No 2044, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. 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^{-4/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in an empirical application.

Keywords: Nonparametric inference; relative efficiency (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2016-06
New Economics Papers: this item is included in nep-ecm and nep-net
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Citations: View citations in EconPapers (6)

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Related works:
Journal Article: Simple and honest confidence intervals in nonparametric regression (2020)
Working Paper: Simple and Honest Confidence Intervals in Nonparametric Regression (2018)
Working Paper: Simple and Honest Confidence Intervals in Nonparametric Regression (2018)
Working Paper: Simple and Honest Confidence Intervals in Nonparametric Regression (2016)
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