Cross-validation for choosing resolution level for nonlinear wavelet curve estimators Hall, Peter en_US Penev, Spiridon en_US 2021-11-25T13:41:28Z 2021-11-25T13:41:28Z 2001 en_US
dc.description.abstract We show that unless the target density is particularly smooth, cross-validation applied directly to nonlinear wavelet estimators produces an empirical value of primary resolution which fails, by an order of magnitude, to give asymptotic optimality. We note, too, that in the same setting, but for different reasons, cross-validation of the linear component of a wavelet estimator fails to give asymptotic optimality, if the primary resolution level that it suggests is applied to the nonlinear form of the estimator. We propose an alternative technique, based on multiple cross-validation of the linear component. Our method involves dividing the region of interest into a number of subregions, choosing a resolution level by cross-validation of the linear part of the estimator in each subregion, and taking the final empirically chosen level to be the minimum of the subregion values. This approach exploits the relative resistance of wavelet methods to over-smoothing: the final resolution level is too small in some parts of the main region, but that has a relatively minor effect on performance of the final estimator. The fact that we use the same resolution level throughout the region, rather than a different level in each subregion, means that we do not need to splice together different estimates and remove artificial jumps where the subregions abut. en_US
dc.description.uri en_US
dc.identifier.issn 1350-7265 en_US
dc.language English
dc.language.iso EN en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.source Legacy MARC en_US
dc.title Cross-validation for choosing resolution level for nonlinear wavelet curve estimators en_US
dc.type Journal Article en
dcterms.accessRights metadata only access
dspace.entity.type Publication en_US
unsw.relation.faculty UNSW Canberra
unsw.relation.faculty Science
unsw.relation.ispartofissue 2 en_US
unsw.relation.ispartofjournal Bernoulli en_US
unsw.relation.ispartofpagefrompageto 317-341 en_US
unsw.relation.ispartofvolume 7 en_US
unsw.relation.originalPublicationAffiliation Hall, Peter, Business, Australian Defence Force Academy, UNSW en_US
unsw.relation.originalPublicationAffiliation Penev, Spiridon, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Business * School of Mathematics & Statistics *
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