A novel criterion is introduced for parametric errors-in-variables identification of stochastic linear systems excited by non-Gaussian inputs. The new criterion is (at least theoretically) insensitive to a class of input-output disturbances because it implicitly involves higher- than second-order cumulant statistics. In addition, it is shown to be equivalent to the conventional Mean-Squared Error (MSE) as if the latter was computed in the ideal case of noise-free input-output data. The sampled version of the criterion converges to the novel MSE and guarantees strongly consistent parameter estimators. The asymptotic behavior of the resulting parameter estimators is analyzed and guidelines for minimum variance experiments are discussed briefly. Informative enough input signals and persistent of excitation conditions are specified. Computatonally attractive Recursive-Least-Squares variants are also developed for on-line implementation of ARMA modeling, and their potential is illustrated by applying them to time-delay estimation in low SNR environment. The performance of the proposed algorithms and comparisons with conventional methods are corroborated using simulated data.