Sufficient Conditions for a Linear Estimator to be a Local Polynomial Regression
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 nonnegative 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 DOI:
 10.48550/arXiv.1803.06050
 arXiv:
 arXiv:1803.06050
 Bibcode:
 2018arXiv180306050S
 Keywords:

 Statistics  Methodology;
 Mathematics  Statistics Theory
 EPrint:
 Manuscript date 1993