Nonparametric estimation of distributions with given marginals via Bernstein–Kantorovich polynomials: and pointwise convergence theory

The copula density is estimated using Bernstein–Kantorovich polynomials. The estimator is the usual one based on the smoothed histogram. Strong consistency is obtained in L 1 and pointwise almost everywhere, allowing for dependent data. For L 1 convergence, no condition is imposed on the copula density, while for pointwise convergence, the condition imposed on the true copula density appears to be minimal.