Symmetric Statistics, Poisson Point Processes, and Multiple Wiener Integrals
Symmetric Statistics, Poisson Point Processes, and Multiple Wiener Integrals
The asymptotic behaviour of symmetric statistics of arbitrary order is studied. As an application we describe all limit distributions of square integrable $U$-statistics. We use as a tool a randomization of the sample size. A sample of Poisson size $N_\lambda$ with $EN_\lambda = \lambda$ can be interpreted as a Poisson …