Monotonicity preservation properties of kernel regression estimators
Statistics Theory
2021-05-13 v2 Statistics Theory
Abstract
Three common classes of kernel regression estimators are considered: the Nadaraya--Watson (NW) estimator, the Priestley--Chao (PC) estimator, and the Gasser--M\"uller (GM) estimator. It is shown that (i) the GM estimator has a certain monotonicity preservation property for any kernel , (ii) the NW estimator has this property if and only the kernel is log concave, and (iii) the PC estimator does not have this property for any kernel . Other related properties of these regression estimators are discussed.
Cite
@article{arxiv.2007.01757,
title = {Monotonicity preservation properties of kernel regression estimators},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:2007.01757},
year = {2021}
}
Comments
A shorter version, without pictures, to appear in Statistics and Probability Letters