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Nonparametric Estimation of Multivariate Distributions with Given Marginals

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dc.contributor.authorSancetta, Alessio
dc.date.accessioned2004-06-16T16:05:26Z
dc.date.available2004-06-16T16:05:26Z
dc.date.created2003-02en_GB
dc.date.issued2004-06-16T16:05:26Z
dc.description.abstractNonparametric estimation of the copula function using Bernstein polynomials is studied. Convergence in the uniform topology is established. From the nonparametric Bernstein copula, the nonparametric Bernstein copula density is derived. It is shown that the nonparametric Bernstein copula density is closely related to the histogram estimator, but has the smoothing properties of kernel estimators. The optimal order of polynomial under the L2 norm is shown to be closely related to the inverse of the optimal smoothing factor for common nonparametric estimator. In order of magnitude, this estimator has variance equal to the square root of other common nonparametric estimators, e.g. kernel smoothers, but it is biased as a histogram estimator.
dc.format.extent391353 bytes
dc.format.mimetypeapplication/pdfen_GB
dc.format.mimetypeapplication/pdf
dc.identifier.doi10.17863/CAM.5420
dc.identifier.urihttp://www.dspace.cam.ac.uk/handle/1810/352
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/352
dc.language.isoeng
dc.publisherFaculty of Economics
dc.relation.ispartofseriesCambridge Working Papers in Economics
dc.rightsAll Rights Reserved
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/
dc.subjectCopula
dc.subjectCourse of Dimensionality
dc.subjectHistogram
dc.subjectNonparametric Estimator
dc.subjectBernstein Polynomial
dc.subject.classificationClassification-JEL: C14, C51
dc.titleNonparametric Estimation of Multivariate Distributions with Given Marginals
dc.typeWorking Paper
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