On shape-preserving wavelet estimators of cumulative distribution functions and densities Dechevsky, Lubomir en_US Penev, Spiridon en_US 2021-11-25T13:41:42Z 2021-11-25T13:41:42Z 1998 en_US
dc.description.abstract In a previous paper we introduced a general class of shapepreserving wavelet approximating operators (approximators) which transform cumulative distribution functions (cdf) and densities into functions of the same type. Empirical versions of these operators are used in this paper to introduce, in an unified way, shape- preserving wavelet estimators of cdf and densities, with a priori prescribed smoothness properties. We evaluate their risk for a variety of loss functions and analyze their asymptotic behavior. We study the convergence rates depending on minimal additional assumptions about the cdf/ density. These assumptions are in terms of the function belonging to certain homogeneous Besov or Triebel- Lizorkin spaces and others. As a main evaluation tool the integral p-modulus of smoothness is used. en_US
dc.identifier.issn 0736-2994 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 On shape-preserving wavelet estimators of cumulative distribution functions and densities en_US
dc.type Journal Article en
dcterms.accessRights metadata only access
dspace.entity.type Publication en_US
unsw.identifier.doiPublisher en_US
unsw.relation.faculty Science
unsw.relation.ispartofissue 3 en_US
unsw.relation.ispartofjournal Stochastic analysis and applications en_US
unsw.relation.ispartofpagefrompageto 423-462 en_US
unsw.relation.ispartofvolume 16 en_US
unsw.relation.originalPublicationAffiliation Dechevsky, Lubomir en_US
unsw.relation.originalPublicationAffiliation Penev, Spiridon, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
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