Optimal bandwidth selection for semi-recursive kernel regression estimators

TL;DR

This paper introduces an automatic bandwidth selection method for semi-recursive kernel regression estimators, demonstrating competitive accuracy and improved computational efficiency over nonrecursive methods through theoretical analysis and empirical validation.

Contribution

It presents a novel automatic bandwidth selection approach for semi-recursive kernel estimators, enhancing computational efficiency while maintaining estimation accuracy.

Findings

Semi-recursive estimators are computationally more efficient.

The proposed method achieves comparable estimation error to nonrecursive estimators.

Simulation and real data confirm the theoretical advantages.

Abstract

In this paper we propose an automatic selection of the bandwidth of the semi-recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and some special stepsizes, the proposed semi-recursive estimators will be very competitive to the nonrecursive one in terms of estimation error but much better in terms of computational costs. We corroborated these theoretical results through simulation study and a real dataset.