Sufficient Conditions for a Linear Estimator to be a Local Polynomial Regression

03/16/2018

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by   Alexander Sidorenko, et al.

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It is shown that any linear estimator that satisfies the moment conditions up to order p is equivalent to a local polynomial regression of order p with some non-negative weight function if and only if the kernel has at most p sign changes. If the data points are placed symmetrically about the estimation point, a linear weighting function is equivalent to the standard quadratic weighting function.