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On optimal kernel choice for deconvolution

Delaigle, Aurore; Hall, Peter

Description

In this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that "optimal" kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that...[Show more]

dc.contributor.authorDelaigle, Aurore
dc.contributor.authorHall, Peter
dc.date.accessioned2015-12-07T22:21:02Z
dc.identifier.issn0167-7152
dc.identifier.urihttp://hdl.handle.net/1885/19854
dc.description.abstractIn this note we show that, from a conventional viewpoint, there are particularly close parallels between optimal-kernel-choice problems in non-parametric deconvolution, and their better-understood counterparts in density estimation and regression. However, other aspects of these problems are distinctly different, and this property leads us to conclude that "optimal" kernels do not give satisfactory performance when applied to deconvolution. This unexpected result stems from the fact that standard side conditions, which are used to ensure that the familiar kernel-choice problem has a unique solution, do not have statistically beneficial implications for deconvolution estimators. In consequence, certain "sub-optimal" kernels produce estimators that enjoy both greater efficiency and greater visual smoothness.
dc.publisherElsevier
dc.sourceStatistics and Probability Letters
dc.subjectKeywords: Bandwidth; Ill-posed problem; Inverse problem; Kernel density estimation; Mean integrated squared error; Non-parametric curve estimation; Statistical smoothing
dc.titleOn optimal kernel choice for deconvolution
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume76
dc.date.issued2006
local.identifier.absfor010404 - Probability Theory
local.identifier.ariespublicationu3488905xPUB10
local.type.statusPublished Version
local.contributor.affiliationDelaigle, Aurore, University of California
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue15
local.bibliographicCitation.startpage1594
local.bibliographicCitation.lastpage1602
local.identifier.doi10.1016/j.spl.2006.04.016
dc.date.updated2015-12-07T08:53:12Z
local.identifier.scopusID2-s2.0-33745837056
CollectionsANU Research Publications

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