Invariance principle for canonical U- and V-statistics based on dependent observations

Abstract

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.