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Multiscale Likelihood Analysis and Complexity Penalized Estimation

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dc.contributor.author Kolaczyk, Eric D.
Nowak, Robert David
dc.creator Kolaczyk, Eric D.
Nowak, Robert David
dc.date.accessioned 2007-10-31T00:50:25Z
dc.date.available 2007-10-31T00:50:25Z
dc.date.issued 2001-08-20
dc.date.submitted 2002-07-27
dc.identifier.uri http://hdl.handle.net/1911/20032
dc.description Journal Paper
dc.description.abstract We describe here a framework for a certain class of multiscale likelihood factorization wherein, in analogy to a wavlet decomposition of an L² function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy to those underlying a standard multiresolution analysis for wavelets, and hence can be viewed as a multiresolution analysis for likelihoods. We then consider the use of the factorizations in the task of nonparametric, complexity penalized likelihood estimation. We study the risk properties of certain thresholding and partitioning estimators, and demonstrate their adaptivity and near-optimality, in a minimax sense over a broad range of function spaces, based on squared Hellinger distance as a loss function. In particular, our results provide an illustration of how properties of classical wavelet-based estimators can be obtained in a single, unified framework that includes models for continuous, count, and categorical data types.
dc.language.iso eng
dc.subject Factorization
Haar bases
Hellinger distance
Kullback-Leibler divergence
minimax
model selection
multiresolution
recursive partitioning
dc.subject.other Wavelet based Signal/Image Processing
Multiscale Methods
dc.title Multiscale Likelihood Analysis and Complexity Penalized Estimation
dc.type Journal Paper
dc.citation.bibtexName article
dc.citation.journalTitle Annals of Statistics
dc.date.modified 2002-07-27
dc.contributor.center Digital Signal Processing (http://dsp.rice.edu/)
dc.subject.keyword Factorization
Haar bases
Hellinger distance
Kullback-Leibler divergence
minimax
model selection
multiresolution
recursive partitioning
dc.type.dcmi Text
dc.identifier.citation E. D. Kolaczyk and R. D. Nowak, "Multiscale Likelihood Analysis and Complexity Penalized Estimation," Annals of Statistics, 2001.

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  • ECE Publications [1046 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.