Simple and Honest Confidence Intervals in Nonparametric Regression

53 Pages Posted: 6 Sep 2018

See all articles by Timothy Armstrong

Timothy Armstrong

Yale University - Cowles Foundation

Michal Kolesár

Princeton University

Multiple version iconThere are 4 versions of this paper

Date Written: August 29, 2018

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.

Keywords: Nonparametric inference, Relative efficiency

JEL Classification: C12, C14

Suggested Citation

Armstrong, Timothy and Kolesár, Michal, Simple and Honest Confidence Intervals in Nonparametric Regression (August 29, 2018). Cowles Foundation Discussion Paper No. 2044R3, Available at SSRN: https://ssrn.com/abstract=3243943 or http://dx.doi.org/10.2139/ssrn.3243943

Timothy Armstrong (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Michal Kolesár

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

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