Constrained recursive kernel density/regression estimation by stochastic quasi-gradient methods
Statistics Theory
2024-09-05 v1 Optimization and Control
Statistics Theory
Abstract
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained estimators are obtained by application of stochastic (quasi)gradient methods to these problems, classical kernel estimates are derived as particular cases. Accuracy and rate of convergence of the obtained estimates are established, and asymptotically optimal estimation procedure parameters are found. The case of moving density/regression is particularly studied.
Cite
@article{arxiv.2406.16550,
title = {Constrained recursive kernel density/regression estimation by stochastic quasi-gradient methods},
author = {Vladimir Norkin and Vladimir Kirilyuk},
journal= {arXiv preprint arXiv:2406.16550},
year = {2024}
}
Comments
To be published in the Springer book series "Studies in Systems, Decision and Control"