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An Adaptive Orthogonal-Series Estimator for Probability Density Functions

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dc.contributor.author Anderson, G. Leigh
de Figueiredo, Rui J.P.
dc.creator Anderson, G. Leigh
de Figueiredo, Rui J.P.
dc.date.accessioned 2007-10-31T00:34:22Z
dc.date.available 2007-10-31T00:34:22Z
dc.date.issued 1978-02-20
dc.date.submitted 2003-10-22
dc.identifier.uri http://hdl.handle.net/1911/19675
dc.description Tech Report
dc.description.abstract Given a sample set X1,...,XN of independent identically distributed real-valued random variables, each with the unknown probability density function f(â ¢), the problem considered is to estimate f from the sample set. The function f is assumed to be in L<sub>2</sub>(a,b); f is not assumed to be in any parametric family. This paper constructs an adaptive "two-pass" solution to the problem: In a pre-processing step (the first pass), a preliminary rough estimate of f is obtained by means of a standard orthogonal-series estimator. In the second pass, the preliminary estimate is used to transform the orthogonal series. The new, transformed orthogonal series is then used to obtain the final estimate. The paper establishes consistency of the estimator and derives asymptotic (large sample set) estimates of the bias and variance. It is shown that the adaptive estimator offers reduced bias (better resolution) in comparison to the conventional orthogonal series estimator. computer simulations are presented which demonstrate the small sample set behavior. A case study of a bimodal density confirms the theoretical conclusions.
dc.description.sponsorship National Science Foundation
dc.description.sponsorship Air Force Office of Scientific Research
dc.language.iso eng
dc.subject pattern recognition
density estimation
nonparametric estimation
orthogonal series
dc.title An Adaptive Orthogonal-Series Estimator for Probability Density Functions
dc.type Tech Report
dc.citation.bibtexName techreport
dc.citation.journalTitle Rice University ECE Technical Report
dc.date.modified 2003-10-22
dc.subject.keyword pattern recognition
density estimation
nonparametric estimation
orthogonal series
dc.citation.issueNumber 7803
dc.type.dcmi Text
dc.identifier.citation G. L. Anderson and R. J. de Figueiredo, "An Adaptive Orthogonal-Series Estimator for Probability Density Functions," Rice University ECE Technical Report, no. 7803, 1978.

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  • ECE Publications [1047 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students