Simple and Honest Confidence Intervals in Nonparametric Regression

Authors

Timothy B. Armstrong
Michal Kolesár

Document Type

Discussion Paper

Publication Date

6-1-2016

CFDP Number

2044R3

CFDP Revision Date

2018-08-01

CFDP Pages

38

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.

Comments

Supplement Materials, 13 pp

Recommended Citation

Armstrong, Timothy B. and Kolesár, Michal, "Simple and Honest Confidence Intervals in Nonparametric Regression" (2016). Cowles Foundation Discussion Papers. 2500.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2500