Recurrent nonparametric estimation of functions from functionals of multidimensional density and their derivatives

Recurrent kernel estimates of functions are considered, which depend on functionals of the multidimensional distribution density and their derivatives, and also their piecewise smooth approximations. The principal part of a mean square error of estimates is found. The suggested approach enables estimating from unique positions, for example, the production function and its characteristics. The comparison is performed of recurrent and common estimates both in asymptotics and at finite volumes of samples.