statistical application of wavelet

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1、TheStatistician(2000)49,Part1,pp.1±29WaveletanalysisanditsstatisticalapplicationsFelixAbramovich,TelAvivUniversity,IsraelTrevorC.BaileyUniversityofExeter,UKandTheofanisSapatinasUniversityofKentatCanterbury,UK[ReceivedFebruary1999.RevisedSeptember1999]Summary.Inr

2、ecentyearstherehasbeenaconsiderabledevelopmentintheuseofwaveletmethodsinstatistics.Asaresult,wearenowatthestagewhereitisreasonabletoconsidersuchmethodstobeanotherstandardtooloftheappliedstatisticianratherthanaresearchnovelty.Withthatinmind,thispapergivesarelativ

3、elyaccessibleintroductiontostandardwaveletanalysisandprovidesareviewofsomecommonusesofwaveletmethodsinstatisticalapplications.Itisprimarilyorientatedtowardsthegeneralstatisticalaudiencewhomaybeinvolvedinanalysingdatawheretheuseofwaveletsmightbeeffective,ratherth

4、antoresearcherswhoarealreadyfamiliarwiththe®eld.Giventhatobjective,wedonotemphasizemathematicalgeneralityorrigourinourexpositionofwaveletsandwerestrictourdiscussiontothemorefrequentlyemployedwaveletmethodsinstatistics.Weprovideextensivereferenceswheretheideasand

5、conceptsdiscussedcanbefollowedupingreaterdetailandgeneralityifrequired.Thepaper®rstestablishessomenecessarybasicmathematicalbackgroundandterminologyrelatingtowavelets.Itthenreviewsthemorewell-establishedapplica-tionsofwaveletsinstatisticsincludingtheiruseinnonpa

6、rametricregression,densityestimation,inverseproblems,changepointproblemsandinsomespecializedaspectsoftimeseriesanalysis.Possibleextensionstotheusesofwaveletsinstatisticsarethenconsidered.Thepaperconcludeswithabriefreferencetoreadilyavailablesoftwarepackagesforwa

7、veletanalysis.Keywords:Changepointanalysis;Densityestimation;Fourieranalysis;Inverseproblems;Nonpara-metricregression;Signalprocessing;Spectraldensityestimation;Timeseriesanalysis;Waveletanalysis1.IntroductionIncontrastwithpapersthataredirectedatresearcherswhoar

8、ealreadyworkinginaspecialized®eld,ourintendedaudiencehereisnotthosewhoareconversantwithwaveletanalysisanditsapplications.Wewishrathertoaddressthosestatisticianswho,al