Invariance principle for canonical U- and V-statistics based on dependent observations
Igor' Semenovich Borisov, V. A. Zhechev · Siberian Advances in Mathematics · 2015
We prove the functional limit theorem, i.e., the invariance principle, for sequences of normalized U - and V -statistics of arbitrary orders with canonical kernels, defined on samples of growing size from a stationary sequence of random variables under the α - or φ -mixing conditions. The corresponding limit stochastic processes are described as polynomial forms of a sequence of dependent Wiener processes with a known covariance.