Weak invariance principle for finite-population U-statistics (Q1099493)

Under the weakest possible conditions, we establish the weak invariance principle for finite-population U-statistics. It is worth to point out that, for sampling without replacement, the sequence of random elements in C[0,1], associated with the sample partial sums or the U-statistics, converges in law to the standard Brownian bridge, but not to the Brownian motion as in the usual case of replacement sampling.