Change-point analysis in increasing dimension

Let { Y k , k ∈ Z } be a d -dimensional stationary process, and g ( d ) = ( g 1 ( Y 1 , … Y n ) , … , g d ( Y 1 , … Y n ) ) t be a collection of estimators for some parameter Ψ ( d ) ∈ R d . Based on the weighted CUSUM process, we discuss several procedures to detect possible changes in Ψ ( d ) , where we explicitly allow d = d n to increase with the sample size n . It is demonstrated that an increase in d n (as n increases) may both lead to a loss or gain in power for testing procedures.