A weighted bootstrap approximation of the maximal deviation of kernel density estimates over general compact sets

This article considers a weighted bootstrap method to approximate the distribution of the maximal deviatiBootstrap-MBR.texon of kernel density estimates over general connected compact sets. The theoretical validity of this approximation is also established. Furthermore, simulation studies show that, depending on the choice of the weights, the proposed weighted bootstrap can have a superior finite-sample performance as compared to both the large-sample theory as well as Efron’s (1979) original bootstrap.