PP Multivariate Random Weighting Method

According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting empirical process. Applying this method, we obtain two kinds of goodness-of-fit test for a multivariate distribution function, i.e., we get the random weighting approximations of PP Kolmogorov Smirnov statistics (PPKS) and PP Smirnov Cramer Von Mises statistics (PPSC), we prove that the asymptotic distribution of PPKS and PPSC are the same as those of their respective random weighting approximations.