Using additional data in nonparametric estimation of density functionals

A range of nonparametric kernel estimates are proposed for density functionals. The range is obtained with an allowance for additional data in the shape of functional of conditional and unconditional densities. These estimates may prove helpful in nonparametric identification of the process (regression) model using parametric description of some probabilistic characteristics of the process. An estimate is provided which is asymptotically normal and optimal in the sense of minimal variance. An adaptive estimate is provided which is asymptotically equivalent to the optimal one. Examples are discussed of estimating the density, regression, and conditional generatrix of moments with an allowance for knowledge of probabilistic characteristics of conditional and unconditional densities.