Subagging for bandwidth selection: a computationally efficient approach to kernel density estimation

Abstract

[Abstract]: Bandwidth selection is a central issue in kernel density estimation. For large datasets, classical selectors such as cross-validation and bootstrap become computationally intensive and may yield bandwidths with high variability. This paper proposes subagging-based versions of several popular selectors, including cross-validation, direct plug-in, and bootstrap methods. These selectors are constructed by computing bandwidths over multiple subsamples (without replacement), rescaling them, and averaging the results. We also introduce a novel regression-based approach, Regression Subbagging (RSB), which extrapolates the optimal bandwidth via a log-log regression, avoiding the need to assume a known convergence rate. We assess statistical accuracy in terms of the mean squared error of the selectors and the corresponding MISE of the resulting kernel estimators, using the optimal bandwidth as a benchmark. Computational efficiency is evaluated via parallel implementations using the parallel and foreach packages in R, reporting speedups as a function of the number of CPU cores. The results confirm that subagging improves or preserves statistical performance while yielding substantial runtime reductions, especially for demanding selectors like cross-validation and bootstrap. The RSB variant, in particular, stands out as a scalable, flexible, and robust solution. The core methods are implemented in the R package baggingbwsel, available on CRAN.