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Nonparametric Estimation of Multivariate Distributions with Given Marginals


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Publication Date: 2004-06-16

Publisher: Faculty of Economics

Language: en_GB

Type: Working Paper

Metadata: Show full item record

Citation: Sancetta, A. (2004). Nonparametric Estimation of Multivariate Distributions with Given Marginals. https://doi.org/10.17863/CAM.5420

Abstract: Nonparametric 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.

Keywords: Copula, Course of Dimensionality, Histogram, Nonparametric Estimator, Bernstein Polynomial, Classification-JEL: C14, C51

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This record's DOI: https://doi.org/10.17863/CAM.5420

This record's URL: http://www.dspace.cam.ac.uk/handle/1810/352https://www.repository.cam.ac.uk/handle/1810/352







Author: Sancetta, Alessio

Source: https://www.repository.cam.ac.uk/handle/1810/352



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