Estimation of Functions of a Distribution Density from Dependent Observations

We propose estimates for functions of a multivariate distribution density to which a sequence of conditional distribution densities of dependent random variables converges, whereas the random variables are observed with an additive dependent noise. The rate of convergence of the deviation moments of the estimates proposed and the principal part of their mean-square deviation are found. It is shown that the estimates of functions of a density have the same rate of convergence as the improved estimates of the density.