Minimax linear estimation at a boundary point

2018

SSRN Journal

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. * We thank Don Andrews, Sebiastian Calonico, Matias Cattaneo, Max Farrell and numerous seminar and conference participants for helpful comments and suggestions. We thank Kwok Hao Lee for research assistance. All remaining errors are our own.

Section: Kernel Efficiencymentioning

confidence: 99%

Simple and Honest Confidence Intervals in Nonparametric Regression

Armstrong¹,

2018

SSRN Journal

“…When

p = 1

, the optimal estimator is a local constant estimator based on the triangular kernel. When

p = 2

, the solution is given in Fuller () and Zhao () for the interior point problem, and in Gao () for the boundary point problem. See Appendix D.2 in the Online Supplemental Material for details.…”

Section: Applicationsmentioning

confidence: 99%

Simple and honest confidence intervals in nonparametric regression

Armstrong

2020

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.We thank Don Andrews, Sebiastian Calonico, Matias Cattaneo, Max Farrell, Christoph Rothe, and numerous seminar and conference participants for helpful comments and suggestions. We thank Kwok Hao Lee for research assistance. All remaining errors are our own.

“…the interior point problem, and in Gao (2018) for the boundary point problem. See Appendix D.2 in the Online Supplemental Material for details.…”

Section: Boundary Pointmentioning

confidence: 99%

Simple and Honest Confidence Intervals in Nonparametric Regression

Armstrong¹,

2018

SSRN Journal

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