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
- Mathematics
- 1993
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
- Mathematics, Computer Science
- 1987
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
- Mathematics
- 1985
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
- Mathematics
- 1979
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…
Robust locally weighted regression and smoothimg
- 1979