CMA Research Report

SRR93-015

Formulae for mean integrated squared error of nonlinear wavelet-based density estimators

Abstract:  We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based density estimators. We show tha, unlike the analogous situation for kernel desnity estimators, this MISE formula is relatively unaffected by assumptions of continuity. In particular, it is available for densitites which are smooth in only a piecewise sense. Another difference is that in the wavelet case the classical MISE formula is only valid for sufficiently small values of the bandwidth. For larger bandwidths MISE assumes a very different form, and hardly varies at all with changing bandwidth. This remarkable property guarantees a high level of robustness against oversmoothing, not encountered in the context of kernel methods. We also use the MISE formula to describe an asymptotically optimal empirical bandwidth selection rule.

AMS Classification:  62G07, 62G20
Date:  July 1993

Download PDF   ( 6.25M scanned )


Return to SRR93 contents