Convergence rates for average square errors for kernel smoothing estimators

Until now integrated square error (ISE) for kernel smoothing estimators has been thoroughly investigated in the context of bandwidth selection,while l ittle work has been done for its alternative, average square error (ASE), m ainly because ASE and ISE have been regarded to be nearly equivalent. In th is paper convergence rate of ASE and difference between ISE and ASE are stu died, which reveals that curse of dimension affects square errors in regres sion setting and there exists a cutoff point in dimension where ASE and ISE are no longer asymptotically equivalent.