The paper deals with extensions of the correlation-based statistical linearization of the input-output mappings of nonlinear systems. The approach is based on considering the stochastic system's input and output as elements of a Hilbert space with an inner product of a general type. A proper choice of the inner product leads to using dispersion functions instead of correlation ones when deriving linearized models. The dispersion functions are much more complete measures of dependence between random processes than the correlation ones and provide eliminating the disadvantages of the correlation-based nonlinear system identification.