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dc.contributor.authorWillett, Rebecca
Nowak, Robert David
dc.creatorWillett, Rebecca
Nowak, Robert David
dc.date.accessioned 2007-10-31T01:10:07Z
dc.date.available 2007-10-31T01:10:07Z
dc.date.issued 2003-08-20
dc.date.submitted 2003-08-27
dc.identifier.urihttps://hdl.handle.net/1911/20454
dc.description Tech Report
dc.description.abstract The 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.
dc.description.sponsorship Office of Naval Research
dc.description.sponsorship Army Research Office
dc.description.sponsorship National Science Foundation
dc.language.iso eng
dc.subjectNonparametric estimation
wavelets
minimax risk
dc.subject.otherWavelet based Signal/Image Processing
Multiscale Methods
dc.title Multiscale Density Estimation
dc.type Report
dc.citation.bibtexName techreport
dc.citation.journalTitle Rice University ECE Technical Report
dc.date.modified 2003-08-27
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)
dc.subject.keywordNonparametric estimation
wavelets
minimax risk
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.citation R. Willett and R. D. Nowak, "Multiscale Density Estimation," Rice University ECE Technical Report, 2003.


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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1289]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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