Estimation of linear functionals of bivariate distributions with parametric marginals

Summary In this paper we construct estimators for linear functionals of bivariate distributions with parametric marginals. Our construction generalizes the construction of efficient estimators given by Peng and Schick (2002) for the case of known marginals. More precisely, we show that in their construction the fixed and known orthonormal bases for the Hilbert spaces of square integrable functions with zero means can now be replaced by estimated orthonormal bases using a n 1/2 -consistent estimator of the parameter.