From Bernstein polynomials to Bernstein copulas

In this paper we review Bernstein and checkerboard copulas for arbitrary dimensions and general grid resolutions in connection with discrete random vectors possessing uniform margins, and point out the relation to tensor product Bernstein operators. We further suggest a pragmatic and effective way to fit the dependence structure of multivariate data to Bernstein copulas via rook copulas, a subclass of checkerboard copulas, which is based on the multivariate empirical distribution.