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Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design

  • Yoichi Arai

    (National Graduate Institute for Policy Studies)

  • Hidehiko Ichimura

    (The University of Tokyo)

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.

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Paper provided by National Graduate Institute for Policy Studies in its series GRIPS Discussion Papers with number 13-09.

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Length: 41 pages
Date of creation: Jun 2013
Date of revision:
Handle: RePEc:ngi:dpaper:13-09
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  1. Guido Imbens & Karthik Kalyanaraman, 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," NBER Working Papers 14726, National Bureau of Economic Research, Inc.
  2. Doug Miller & Jens Ludwig, 2005. "Does Head Start Improve Children’s Life Chances? Evidence from a Regression Discontinuity Design," Working Papers 534, University of California, Davis, Department of Economics.
  3. Jens Ludwig & Douglas L Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, MIT Press, vol. 122(1), pages 159-208, 02.
  4. Yoichi Arai & Hidehiko Ichimura, 2013. "Optimal bandwidth selection for differences of nonparametric estimators with an application to the sharp regression discontinuity design," CeMMAP working papers CWP27/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
  6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
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