Random weighting approximation for empirical processes and their applications (Q5917745)

Consider random weighting empirical processes indexed by a bounded class of functions. The authors prove that random weighting empirical processes and empirical processes have the same limit distribution almost surely. Therefore random weighting empirical processes can be applied to simulate empirical processes. In addition, they derive the conditional strong uniform convergence rates of random weighting empirical processes. As an application, when unknown multivariate underlying distribution is not confined by any condition, the authors obtain the random weighting approximations of the multivariate von Mises statistics and their projection pursuit statistics. The authors point out that there are also similar results for the bootstrapped von Mises statistics and their projection pursuit statistics.