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Corpus ID: 88523437

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

@article{Sidorenko2018SufficientCF,
title={Sufficient Conditions for a Linear Estimator to be a Local Polynomial Regression},
author={Alexander Sidorenko and Kurt S. Riedel},
journal={arXiv: Methodology},
year={2018}
}

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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It is proved that in the fixed design regression model, given a weighted local regression procedure with any weight function, there is a corresponding kernel method such that the quotients of weights distributed by both methods tend uniformly to 1 as the number of observations increases to infinity.Expand

The aim of this note is to give a lower bound for the number of sign changes of a real function. This bound depends on the sequence of moments. Several results are known along these lines. However,… Expand

Abstract The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for… Expand