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Nonparametric methods for deconvolving multiperiodic functions

Hall, Peter; Yin, Jiying

Description

Multiperiodic functions, or functions that can be represented as finite additive mixtures of periodic functions, arise in problems related to stellar radiation. There they represent the overall variation in radiation intensity with time. The individual periodic components generally correspond to different sources of radiation and have intrinsic physical meaning provided that they can be 'deconvolved' from the mixture. We suggest a combination of kernel and orthogonal series methods for...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorYin, Jiying
dc.date.accessioned2015-12-13T22:35:10Z
dc.date.available2015-12-13T22:35:10Z
dc.identifier.issn1369-7412
dc.identifier.urihttp://hdl.handle.net/1885/76469
dc.description.abstractMultiperiodic functions, or functions that can be represented as finite additive mixtures of periodic functions, arise in problems related to stellar radiation. There they represent the overall variation in radiation intensity with time. The individual periodic components generally correspond to different sources of radiation and have intrinsic physical meaning provided that they can be 'deconvolved' from the mixture. We suggest a combination of kernel and orthogonal series methods for performing the deconvolution, and we show how to estimate both the sequence of periods and the periodic functions themselves. We pay particular attention to the issue of identifiability, in a nonparametric sense, of the components. This aspect of the problem is shown to exhibit particularly unusual features, and to have connections to number theory. The matter of rates of convergence of estimators also has links there, although we show that the rate-of-convergence problem can be treated from a relatively conventional viewpoint by considering an appropriate prior distribution for the periods.
dc.publisherAiden Press
dc.sourceJournal of the Royal Statistical Society Series B
dc.subjectKeywords: Astronomy; Convergence rate; Folding; Kernel methods; Model identification; Nonparametric curve estimation; Number theory; Orthogonal series methods; Periodic function; Signal analysis; Smoothing; Trigonometric series
dc.titleNonparametric methods for deconvolving multiperiodic functions
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume65
dc.date.issued2003
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub5275
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationYin, Jiying, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage869
local.bibliographicCitation.lastpage886
local.identifier.doi10.1046/j.1369-7412.2003.00420.x
dc.date.updated2015-12-11T09:26:41Z
local.identifier.scopusID2-s2.0-0242550822
CollectionsANU Research Publications

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