Optimal Bandwidth Selection for Kernel Regression Using a Fast Grid Search and a GPU

This study presents a new algorithm and corresponding statistical package for estimating optimal bandwidth for a nonparametric kernel regression. Kernel regression is widely used in Economics, Statistics, and other fields. The formula for the optimal "bandwidth," or smoothing parameter, is well-known. In practice, however, the computational demands of estimating the optimal bandwidth have historically been prohibitively high. Consequently, researchers typically select bandwidths for kernel regressions using ad hoc rules of thumb. This paper exploits the Single Program Multiple Data (SPMD) parallelism inherent in optimal bandwidth calculation to develop a method for computing optimal bandwidth on a GPU. Using randomly generated datasets of different sizes, this approach is shown to reduce the run time by as much as a factor of seven.