Sampling Properties of U-statistics for a Class of Stationary Nonlinear Processes

摘要

We consider the sampling properties of U-statistics based on a sample of realization from a class of stationary nonlinear processes which include, in particular, linear, bilinear and finite order volterra processes. It is shown that if the size n of the realization tends to infinity then certain normalized versions of the U-statistics tend to be distributed normally with zero means and finite variances.