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Minimax Linear Estimation at a Boundary Point

Wayne Yuan Gao

arXiv 18 Oct 2017 · Econometrics · publishedJournal of Multivariate Analysis (2017) · 1 citations (OpenAlex)

arXiv:1710.06809 · PDF · DOI · OpenAlex · Extracted main text

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 second-order H\"{o}lder class). 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.

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1Optimal estimation for regression discontinuity design with binary outcomes0.40511