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Minimax linear estimation at a boundary point

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  • Gao, Wayne Yuan

Abstract

This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is Lipschitz continuous. The result is then applied to construct the minimax optimal estimator for the regression discontinuity design model, where the parameter of interest involves function values at boundary points.

Suggested Citation

  • Gao, Wayne Yuan, 2018. "Minimax linear estimation at a boundary point," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 262-269.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:262-269
    DOI: 10.1016/j.jmva.2018.01.001
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    References listed on IDEAS

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    1. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    2. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 79-99, March.
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    Cited by:

    1. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.

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