An Adaptive Orthogonal-Series Estimator for Probability Density Functions

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dc.citation.bibtexNametechreporten_US
dc.citation.issueNumber7803en_US
dc.citation.journalTitleRice University ECE Technical Reporten_US
dc.contributor.authorAnderson, G. Leighen_US
dc.contributor.authorde Figueiredo, Rui J.P.en_US
dc.date.accessioned2007-10-31T00:34:22Z
dc.date.available2007-10-31T00:34:22Z
dc.date.issued1978-02-20
dc.date.modified2003-10-22en_US
dc.date.submitted2003-10-22en_US
dc.descriptionTech Reporten_US
dc.description.abstractGiven 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.en_US
dc.description.sponsorshipNational Science Foundationen_US
dc.description.sponsorshipAir Force Office of Scientific Researchen_US
dc.identifier.citationG. L. Anderson and R. J. de Figueiredo, "An Adaptive Orthogonal-Series Estimator for Probability Density Functions," <i>Rice University ECE Technical Report,</i> no. 7803, 1978.
dc.identifier.urihttps://hdl.handle.net/1911/19675
dc.language.isoeng
dc.subjectpattern recognition*
dc.subjectdensity estimation*
dc.subjectnonparametric estimation*
dc.subjectorthogonal series*
dc.subject.keywordpattern recognitionen_US
dc.subject.keyworddensity estimationen_US
dc.subject.keywordnonparametric estimationen_US
dc.subject.keywordorthogonal seriesen_US
dc.titleAn Adaptive Orthogonal-Series Estimator for Probability Density Functionsen_US
dc.typeReport
dc.type.dcmiText
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