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 little work has been done for its alternative, average square error (ASE), mainly because ASE and ISE have been regarded to be nearly equivalent. In this paper convergence rate of ASE and difference between ISE and ASE are studied, which reveals that curse of dimension affects square errors in regression setting and there exists a cutoff point in dimension where ASE and ISE are no longer asymptotically equivalent.