Orthogonal series and limit theorems for canonical U-and V-statistics of stationary connected observations

Abstract

The limit behavior is studied for the distributions of normalized U-and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying φ-or α-mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.