Non-parametric Procedures under Estimating Stochastic Dependencies in Nonlinear Systems

摘要

In the paper, a measure of dependence coupling k pairs of random processes is introduced. Such a measure, based on using conditional mathematical expectations of the processes, may be considered as a further generalization of the dispersion (variance) functions. Convergence with probability 1 of nonparametric estimates of such a measure is derived using sampled data. These estimates are applied to deriving sampled analogues of some nonlinear measures of stochastic dependence of random processes, in particular, to a consistent, in the Kolmogorov sense, measure of dependence.