Nonparametric estimation of distributions with given marginals via Bernstein–Kantorovich polynomials: L1 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 L1 and pointwise almost everywhere, allowing for dependent data. For L1 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.