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

2018/03/16 by Sidorenko, Alexander, Riedel, Kurt S.
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1803.06050

Abstract

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.

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