Nonparametric Estimation of Multivariate Distributions with Given Marginals

Alessio Sancetta

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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: Bernstein Polynomial; Copula; Course of Dimensionality; Histogram; Nonparametric Estimator. (search for similar items in EconPapers)
JEL-codes: C14 C51 (search for similar items in EconPapers)
Pages: 34
Date: 2003-02
New Economics Papers: this item is included in nep-ecm
Note: EM
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:0320

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