Bagging cross-validated bandwidths with application to Big Data

Hall and Robinson (2009) proposed and analyzed the use of bagged cross-validation to choose the bandwidth of a kernel density estimator. They established that bagging greatly reduces the noise inherent in ordinary cross-validation, and hence leads to a more efficient bandwidth selector. The asymptotic theory of Hall and Robinson (2009) assumes that $N$, the number of bagged subsamples, is $\infty$. We expand upon their theoretical results by allowing $N$ to be finite, as it is in practice. Our results indicate an important difference in the rate of convergence of the bagged cross-validation bandwidth for the cases $N=\infty$ and $N<\infty$. Simulations quantify the improvement in statistical efficiency and computational speed that can result from using bagged cross-validation as opposed to a binned implementation of ordinary cross-validation. The performance of thebagged bandwidth is also illustrated on a real, very large, data set. Finally, a byproduct of our study is the correction of errors appearing in the Hall and Robinson (2009) expression for the asymptotic mean squared error of the bagging selector.