Two-sample <i>U</i>-statistic processes for long-range dependent data
Two-sample <i>U</i>-statistic processes for long-range dependent data
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),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. …