On extension of nonlinear residual transformation class for recursive algorithms of parametric estimation

The problem of estimating the parameters of regression and autoregression processes with random moving-average perturbations is discussed. The estimates are formed by a stochastic-gradient method based on nonlinear transformation of a “generalized deviation”. A class of operators that form a dependent noise is isolated for which the discussed algorithms have a guaranteed strong consistency for any monotonic deviation transformation including signum (on-off) functions.