Bagging cross-validated bandwidths with application to big data

Hall & Robinson (2009) proposed and analysed 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 & 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