Nonparametric Estimation of Multivariate Distributions with Given Marginals
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Authors
Sancetta, Alessio
Publication Date
2004-06-16Series
Cambridge Working Papers in Economics
Publisher
Faculty of Economics
Language
en_GB
Type
Working Paper
Metadata
Show full item recordCitation
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
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.5420
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