Bootstrapping point processes with some applications

We study the weak limit behavior of certain types of point processes obtained by replacing the original observations by the bootstrap sample. The usual bootstrap fails asymptotically in cases for which there exists a Poisson point process or a fixed point measure in the limit. In some cases, by subsampling at the rate m=m(n)=o(n)→∞ in the bootstrap (where n is the sample size), this problem will be resolved and convergence holds in probability. If m log log n/n→0 then asymptotic results are valid almost surely. The method is applied to some statistical problems.