Change-point analysis in increasing dimension

Let {Yk,k∈Z} be a dd-dimensional stationary process, and g(d)=(g1(Y1,…Yn),…,gd(Y1,…Yn))t be a collection of estimators for some parameter Ψ(d)∈Rd. Based on the weighted CUSUM process, we discuss several procedures to detect possible changes in Ψ(d), where we explicitly allow d=dnd=dn to increase with the sample size nn. It is demonstrated that an increase in dndn (as nn increases) may both lead to a loss or gain in power for testing procedures.