Almost sure representations of weighted U-statistics with applications

摘要

LetX_1.....X_n be a sample of i.i.d. random variables on the real line. In this paper, we introduce and study weighted U-statistics of the type S_n = (n(n - 1))~(-1) Σ_(i≠j)J(i+1,j+1) h (X_(i:n), X_(j:n)), where J and h are given bivariate functions