An approach is presented that allows solving the problems of synthesis and analysis of non-parametric nuclear estimates for most practical characteristics of conditional and unconditional distributions. All results are generalized to the case of dependent stationary observations. Questions of convergence of estimates in different metrics are investigated. Versions of non-parametric nuclear estimates with high rate of convergence are proposed. The developed apparatus is applied to signal processing tasks under conditions of non-parametric a priori uncertainty. For professionals involved in information processing, management, forecasting, filtering and using estimation methods in conditions of significant a priori uncertainty.