THE BERNSTEIN COPULA AND ITS APPLICATIONS TO MODELING AND APPROXIMATIONS OF MULTIVARIATE DISTRIBUTIONS

Alessio Sancetta and Stephen Satchell

Econometric Theory, 2004, vol. 20, issue 3, 535-562

Abstract: We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of Bernstein copulas. Rates of consistency when the Bernstein copula density is estimated empirically are given. In order of magnitude, this estimator has variance equal to the square root of the variance of common nonparametric estimators, e.g., kernel smoothers, but it is biased as a histogram estimator.We would thank Mark Salmon for interesting us in the copula function and Peter Phillips, an associate editor, and the referees for many valuable comments. All remaining errors are our sole responsibility.

Date: 2004
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