Nguyen Van Toan
 
Abstract
In this paper we obtain the weak convergence of the bootstrap empirical process with random resample size. The proof is based on the use of dual Lipschitz metric, defined by the weak topology on the space of probability measures on $D$, where $D$ is the space of all real-valued functions $f$ on $[-\infty,\infty]$, such that $f$ vanishes continuously at $\pm\infty$ and is right continuous with left limits on $(-\infty,\infty)$.