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Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design
en
Bandwidth selection
kernel density estimation
local linear regression
regression discontinuity design
ARAI Yoichi
ICHIMURA Hidehiko
政策研究大学院大学 / National Graduate Institute for Policy Studies
東京大学 / Department of Economics, The University of Tokyo
経済学 / Economics
We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimization problem is not well-defined when the sign of the product of the second derivatives of the underlying functions at the estimated points is positive. To address this problem, we theoretically define and construct estimators of the asymptotically first-order optimal (AFO) bandwidths which are well-defined regardless of the sign. They are based on objective functions which incorporate a second-order bias term. Our approach is general enough to cover estimation problems related to densities and regression functions at interior and boundary points. We provide a detailed treatment of the sharp regression discontinuity design.
GRIPS Discussion Papers
13-09
2013-06
GRIPS Policy Research Center
https://ideas.repec.org/p/ngi/dpaper/13-09.html|https://ideas.repec.org/p/ngi/dpaper/13-09.html
http://www.grips.ac.jp/list/jp/facultyinfo/arai_yoichi/|http://www.grips.ac.jp/list/jp/facultyinfo/arai_yoichi/