Motivated by some common-change point tests, we investigate the asymptotic
distribution of the U-statistic process
Unβ(t)=βi=1[nt]ββj=[nt]+1nβh(Xiβ,Xjβ), 0β€tβ€1, when
the underlying data are long-range dependent. We present two approaches, one
based on an expansion of the kernel h(x,y) into Hermite polynomials, the
other based on an empirical process representation of the U-statistic.
Together, the two approaches cover a wide range of kernels, including all
kernels commonly used in applications