Bootstrapping point processes with some applications

We study the weak limit behavior of certain types of point processes obtain ed by replacing the original observations by the bootstrap sample. The usua l 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 subs ampling at the rate m = m(n) = o(n) --> infinity 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 almo st surely. The method is applied to some statistical problems. (C) 1999 Els evier Science B.V. All rights reserved.