Recursive kernel density estimators under missing data

TL;DR

This paper introduces an automatic bandwidth selection method for recursive kernel density estimators with missing data, demonstrating improved accuracy and efficiency over nonrecursive methods through theoretical analysis and simulations.

Contribution

It proposes a novel automatic bandwidth selection procedure for recursive kernel density estimators handling missing data, enhancing estimation accuracy and computational efficiency.

Findings

Recursive estimators outperform nonrecursive ones in estimation error for global density.

Recursive estimators are significantly faster computationally.

Simulation studies confirm theoretical advantages.

Abstract

In this paper we propose an automatic bandwidth selection of the recursive kernel density estimators with missing data in the context of global and local density estimation. We showed that, using the selected bandwidth and a special stepsize, the proposed recursive estimators outperformed the nonrecursive one in terms of estimation error in the case of global estimation. However, the recursive estimators are much better in terms of computational costs. We corroborated these theoretical results through simulation studies and on the simulated data of the Aquitaine cohort of HIV-1 infected patients and on the coriell cell lines using the chromosome number 11.