Uniform Limit Theorem and tail estimates for parametric u-statistics
  We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space.   We obtain also a non-asymptotic and non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for the uniform norm of centered and naturally normed deviation of u-statistics by means of its martingale representation.   Our results are formulated in a very popular and natural terms of metric entropy in the distance (distances) generated by the introduced random processes (fields). 
E.Ostrovsky, L.Sirota
math.ST stat.TH