Multiscale Density Estimation

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dc.citation.bibtexNametechreporten_US
dc.citation.journalTitleRice University ECE Technical Reporten_US
dc.contributor.authorWillett, Rebeccaen_US
dc.contributor.authorNowak, Robert Daviden_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T01:10:07Z
dc.date.available2007-10-31T01:10:07Z
dc.date.issued2003-08-20en
dc.date.modified2003-08-27en_US
dc.date.submitted2003-08-27en_US
dc.descriptionTech Reporten_US
dc.description.abstractThe nonparametric density estimation method proposed in this paper is computationally fast, capable of detecting density discontinuities and singularities at a very high resolution, spatially adaptive, and offers near minimax convergence rates for broad classes of densities including Besov spaces. At the heart of this new method lie multiscale signal decompositions based on piecewise-polynomial functions and penalized likelihood estimation. Upper bounds on the estimation error are derived using an information-theoretic risk bound based on squared Hellinger loss. The method and theory share many of the desirable features associated with wavelet-based density estimators, but also offers several advantages including guaranteed non-negativity, bounds on the L1 error, small-sample quantification of the estimation errors, and additional flexibility and adaptability. In particular, the method proposed here can adapt the degrees as well as the locations of the polynomial pieces. For a certain class of densities, the error of the variable degree estimator converges at nearly the parametric rate. Experimental results demonstrate the advantages of the new approach compared to traditional density estimators and wavelet-based estimators.en_US
dc.description.sponsorshipOffice of Naval Researchen_US
dc.description.sponsorshipArmy Research Officeen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.identifier.citationR. Willett and R. D. Nowak, "Multiscale Density Estimation," <i>Rice University ECE Technical Report,</i> 2003.
dc.identifier.urihttps://hdl.handle.net/1911/20454
dc.language.isoeng
dc.subjectNonparametric estimation*
dc.subjectwavelets*
dc.subjectminimax risk*
dc.subject.keywordNonparametric estimationen_US
dc.subject.keywordwaveletsen_US
dc.subject.keywordminimax risken_US
dc.subject.otherWavelet based Signal/Image Processingen_US
dc.subject.otherMultiscale Methodsen_US
dc.titleMultiscale Density Estimationen_US
dc.typeReport
dc.type.dcmiText
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