ernstein estimators attracted considerable attention as smooth nonpara-
metric estimators for distribution functions, densities, copulas and copula densities.
The present paper adds a parallel result for the first-order derivative of a copula
function. This result then leads to Bernstein estimators for a conditional distribution
function and its important functionals such as the regression and quantile functions.
Results of independent interest have been derived such as an almost sure oscillation
behavior of the empirical copula process and a Bahadur-type almost sure asymptotic
representation for the Bernstein estimator of a regression quantile function. Simula-
tions demonstrate the good performance of the proposed estimators.

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• Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals