Tail Probabilities and Its Convergence Rate for B-Valued U-Statistics

Let B be separable Banach spaces, （S，S，P）a probalility measure spaces and H（x₁…,x_m）:S^m→B a measurable function symmetric in its arguments. In this paper we discuss tail probabilities for B-valued U-statistics U_mⁿHbased on P and H, which may be viewed as an extension of the corresponding i.i.d case.