• 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. 

References

SHOWING 1-7 OF 7 REFERENCES
Local Regression: Automatic Kernel Carpentry
A kernel smoother is an intuitive estimate of a regression function or conditional expectation; at each point xO the estimate of E(YIxo) is a weighted mean of the sample Yi, with observations close
Weighted Local Regression and Kernel Methods for Nonparametric Curve Fitting
TLDR
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.
On the number of sign changes of a real function
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,
Robust Locally Weighted Regression and Smoothing Scatterplots
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
Variable Bandwidth and Local Linear Regression Smoothers
Robust locally weighted regression and smoothimg
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