A new preprint joint with Aeneas Rooch about “Two-sample U-statistic processes for long-range dependent data” is online at arXiv.

Abstract: Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process $U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j)$, 0≤t≤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.