A Nonparametric Measure of Dependence in the Statistical Linearization

The paper presents an approach to the statistical linearization of the input/output mapping of non-linear discrete-time stochastic systems driven by a white-noise Gaussian process. The approach is based on applying the contingency coefficient, a nonparametric measure of dependence. Within such an approach, the statistical linearization criterion is the condition of coincidence of the mathematical expectations of the output processes of the system under study and the derived model and the condition of coincidence of the contingency coefficient of the input and output processes of the system and the contingency coefficient of the input and output processes of the model. As a result, explicit analytical expressions to derive coefficients of the weight function of the target linearized model are obtained. The consideration is preceded with an analysis of applying consistent measures of dependence within the system identification.