  Motivated by challenges on studying a new correlation measurement being
popularized in evaluating online ranking algorithms' performance, this
manuscript explores the validity of uncertainty assessment for weighted
U-statistics. Without any commonly adopted assumption, we verify Efron's
bootstrap and a new resampling procedure's inference validity. Specifically, in
its full generality, our theory allows both kernels and weights asymmetric and
data points not identically distributed, which are all new issues that
historically have not been addressed. For achieving strict generalization, for
example, we have to carefully control the order of the "degenerate" term in
U-statistics which are no longer degenerate under the empirical measure for
non-i.i.d. data. Our result applies to the motivating task, giving the region
at which solid statistical inference can be made.
