Constrained recursive kernel density/regression estimation by stochastic quasi-gradient methods

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...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Norkin, Vladimir, Kirilyuk, Vladimir
Format: Article
Language:English
Subjects:
Density
Estimates
Optimization
Regression
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2406.16550