Weak and strong representations for quantile processes from finite populations with application to simulation size in resampling inference

We prove three results on the weak or strong representations for quantile processes of samples drawn randomly with or without replacement from a finite population. As an application of the strong‐approximation result (Theorem 2), we give an approach for determining the order of B , the number of Monte Carlo simulations required for the accuracy of resampling inference. In typical situations the order of B is between nb n and n 2+δ , where n is the original sample size, δ > 0, and (log log n )/ b n → 0.