THE BERNSTEIN COPULA AND ITS APPLICATIONS TO MODELING AND APPROXIMATIONS OF MULTIVARIATE DISTRIBUTIONS
伯恩斯坦 Copula 及其在多元分布建模与逼近中的应用
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…