On one approach tо investigation of functionals of conditional distributions under statistical uncertainty

The paper is concerned with a method for design of nonparametric estimates of functionals of conditional distributions where a priori data on the form of the distribution function which specifies sampled observations are not available. Asymptotic properties of the proposed estimates are studied; their limit distributions are found an their r. m. s. convergence to the functions to be estimates are proven; some optimization aspects are treated.