English

Two-Sample U-Statistic Processes for Long-Range Dependent Data

Probability 2014-04-03 v1

Abstract

Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process Un(t)=i=1[nt]j=[nt]+1nh(Xi,Xj)U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j), 0t10\leq t\leq 1, when the underlying data are long-range dependent. We present two approaches, one based on an expansion of the kernel h(x,y)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.

Keywords

Cite

@article{arxiv.1404.0551,
  title  = {Two-Sample U-Statistic Processes for Long-Range Dependent Data},
  author = {Herold Dehling and Aeneas Rooch and Martin Wendler},
  journal= {arXiv preprint arXiv:1404.0551},
  year   = {2014}
}
R2 v1 2026-06-22T03:41:10.762Z