ON LIMITING PROPERTIES OF U-STATISTICS AND VON-MISES STATISTICS
X Chen · 1980
In this paper, assume that the r-th moment of the kernel is finite, then we obtain the order of the r-th moment of U-statistics. Using this result, we get under the above assumption the complete solution of the rate of convergence of U-statistics, and derive a formula, which establishes the connection between U-statistics and the closely-related vou-Mises statistics. This will be employed to obtain the rate of convergence of von-Mises statistics and particularly to obtain the Berry-Esseen hound for von-Mises statistics only in the case of finite moment of third order.